A paperless classroom activity. 00 PDF This quiz assesses how well students can find the missing side length of a shape when given a another shape that is similar. The two triangles pictured below are similar. Finding missing sides of congruent triangles worksheet Congruent Exactly equal in size and shape. T Worksheet by Kuta Software LLC. Finding Missing Sides of Similar Figures Worksheet. Great for a quick check to . 11-6 - Find Missing Side - Similar Triangles. J A M h 1 D E B h 2 60 126 40 68 18. Solve real-life problems involving similar triangles. You may select equilateral, right scalene, right isosceles, obtuse scalene, obtuse isosceles, acute scalene and acute isosceles. This worksheet and lesson series with have students find missing lengths of triangles mostly through the help of the pythagorean theorem. ID 11 Practice Ch. If so, state how you know they are similar and complete the. Includes slides with a matching handout and a worksheet. 7) similar; SSS similarity; QRS8) not similar Find the missing length. Suppose that h 148. Worksheets are Similar triangles date period, S. Step 1 Given a pair of similar triangles, determine which sides correspond to each other. Worksheet by Kuta Software LLC. Similar Triangles Worksheet A follow up worksheet for extra practice, where students have to work out missing sides in similar triangles. Finding Missing Sides Of Similar Triangles Activity Similar Figures - Polygons that have the same shape, but different size. t Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name Similar Triangles Date Period State if the triangles in each pair are similar. Similar Triangle Worksheet 1. Identifying Similar Triangles When the altitude is drawn to the hypotenuse of a right triangle, the two smaller triangles are similar to the original triangle and to each other. Triangles are strong because of their inherent structural characteristics. This set of Boom Cards features 40 different Digital Self-Checking Task Cards. Algebra 1 - Mr. - Finding Missing Sides and Angles. Similar Figures. Perimeter of a Triangle Worksheets. com t t t t K L M t t t A B C. Similar Figures. Finding Missing Sides - Similar Triangle Practice worksheet. L Worksheet by Kuta Software LLC Geometry ID 1. Have each student from a team go to a different corner of the room depending on their number (1-4) to meet with other. L Worksheet by Kuta Software LLC Geometry ID 1 Name Date Period e G2t0 s1N3T pK Ou4t war WShoTf vtqw9aIr Be k cL ALlC j. 2 in 6. You may select equilateral, right scalene, right isosceles, obtuse scalene, obtuse isosceles, acute scalene and acute isosceles. t Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name Similar Triangles Date Period State if the triangles in each pair are similar. Try the free Mathway calculator and problem solver below to practice various math topics. E p 6A 6l zl w IrHiJg ahDt7s c 5r Mevsmelr 3vhe Udj. We compare the ratios and find the length of the unknown side of the triangle. Examples, videos, worksheets, and solutions to help Grade 8 students learn how to find missing sides and angles of similar triangles. 4 faces the angle marked with two arcs as does the side of length 8 in triangle R. The smallest side of the first triangle corresponds to the smallest. Worksheets are Similar figures date period, Solving proportions involving similar figures, Similar triangle work, Similar figures, Finding missing lengths of similar triangles, Finding unknown measures in similar figures, 7 using similar polygons, Work similar triangles. Similar Figures. 5 Google Classroom Solve for x x. Persons 1 does problem 1. Find the missing length. Similar Figures - Polygons that have the same shape, but different size. L Worksheet by Kuta Software LLC Geometry ID 1 Name Date Period e G2t0 s1N3T pK Ou4t war WShoTf vtqw9aIr Be k cL ALlC j. 42 If a 36-inch yardstick casts a 21 -foot shadow, how tall is a building whose shadow is 168 feet (Draw a picture with two similar polygons. V 3 sMia bd3e e aw7iStzh y EIn1fpi Ensizt3e 5 LG1eXodm YehtDrJy w. 7 14 A B C 6) 5 B 4 A C 7) 11 4. Finding the missing side. 17) 60 50 B D C 11 x 4 70 S R T 8 18) 21 30 E F D 77 11 x 11 A C B 9 19) 64 96 72 J K L 4. Algebra 1 - Mr. Similar Triangles - Missing Sides with Algebraic Expressions Practice. Similar Triangles - Missing. (ii) Find the lengths of the missing sides. Triangles have two kinds of angles interior and exterior. 9 10 B A C 5) 7. N W2h0 S1P12 6K Pu CtcaN TS woPfytzw ya Jr de F 0L2LfCN. Examples, videos, worksheets, and solutions to help Grade 8 students learn how to find missing sides and angles of similar triangles. find the missing measurements of two similar figures. Materials Overhead of figures for the Similarity Basketball Game Trash can or box for basketball goal, and a foam ball Masking tape for shooting line. Similar Triangle Missing Side Worksheets - total of 8 printable worksheets available for this concept. Page 2. Find the perimeter. State if the triangles in each pair are similar. How to Find the Missing Sides of Similar Triangles. Cut apart and use for a single student or pair of students. 4 A B C 8) 3 3 B C A Find the measure of each side indicated. How to Find the Missing Sides of Similar Triangles. Find the Missing Sides for the Pair of Similar Triangles. Similar Shapes Finding Sides Textbook Exercise Corbettmaths October 7, 2019 corbettmaths Similar Shapes Finding Sides Textbook Exercise Click here for. Find the missing side and angle. Similar Triangles Worksheets. Worksheet by Kuta Software LLC. In this deck, students will be practicing finding the missing sides of similar figures. If so, state how you know they are similar and complete the. All equilateral triangles or squares with any side length are examples of similar objects. Finding Missing Sides - Similar Triangle Practice pwelch Member for 3 years 1 month Age 13-18 Level 9-12 Language English (en) ID 848133 23032021 Country code US Country United States School subject Math (1061955) Main content Triangles (2012002) Finding Missing Sides - Similar Triangle Practice Share Print Worksheet Finish. Triangle Angle Sum Worksheet. ) Sam wants to enlarge a triangle with sides 3, 6 and 6 inches. If the shortest side of the new triangle is 13 inches, how long will the other two sides be. 9 ft. Find the missing length. In the earlier examples, we evaluated the sine and cosine on triangles where we knew all three sides of the triangle. Find the missing side lengths in each pair of similar figures. Similar triangles are triangles that. If so, state how you know they are similar and complete the. W Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name Using Similar Polygons Date Period. Similar Triangles Missing Side Practice Teaching Resources Homework for Using Proportions to find missing sides in Similar Triangles designed for Google Sheets. 4 Y kARl Ml3 Xr LiBgrh atJsZ Tr MeZs te crDv he Ld L. X ,y 5. Unknown Side Lengths in Right Triangles Worksheets. Each pair of figures is similar. The set includes 18 pairs of matching cards (18 problems of all types)one side with diagram of triangles, the other side a segment measure. Similar Figures - Polygons that have the same shape, but different size. 3) Convert the followings a) 5cm into mm. 11-6 - Find Missing Side - Similar Triangles. Put the measurements of the smaller figure on top and the bigger figure on the bottom. V 3 sMia bd3e e aw7iStzh y EIn1fpi Ensizt3e 5 LG1eXodm YehtDrJy w. Find the missing angle in each triangle. The smallest side of the first triangle corresponds to the smallest. Missing Sides and Angles of Similar Triangles Related Topics More Lessons for Grade 8 Math Math Worksheets Examples, videos, worksheets, and solutions to help Grade 8 students learn how to find missing sides and angles of similar triangles. Adjacent, Opposite and Hypotenuse, in a right triangle is shown below. P SIM 07 HW63b State if the triangles in each pair are similar. a)Find h 2. Chapter 11. Triangle Angle Sum Worksheets This Triangle Worksheet will produce triangle angle sum problems. Example 1 The figures in each pair are similar Example 2 The figures in each pair are similar (ABC XYZ). Give each student the Similar Triangles-Finding Missing Measures worksheet. Math HSG. Algebra 1 - Mr. a)Find h 2. &92;triangle QRS QRS only. Maths Trigonometry missing sides worksheet Subject Mathematics Age range 14-16 Resource type WorksheetActivity 35. 11-6 - Find Missing Side - Similar Triangles. C) Each pair of triangles is similar. Click on Open button to open and print to worksheet. The names change depending on which angle is the focus angle. Geometry online exercise. x Practice Problems Find the missing side(s) in each similar figure. Each pair of figures is similar. This worksheet is a great resources for the 5th, 6th Grade, 7th Grade, and 8th Grade. ID 11 Practice Ch. Each pair of figures is similar. E p 6A 6l zl w IrHiJg ahDt7s c 5r Mevsmelr 3vhe Udj. Two rectangles are similar. P SIM 07 HW63b State if the triangles in each pair are similar. Use geometric means. If so, state how you know they are similar and complete the. 11-6 - Find Missing Side - Similar Triangles. Then work the problem on this card. Identifying Similar Triangles Identify the similar triangles in the diagram. small small big big The missing side is . Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. The smallest side of the first triangle corresponds to the smallest. Kuta Software - Infinite Geometry Similar Right Triangles Name Date Period Find the missing length indicated. 85 KB A. Offered in this set of pdf worksheets are the scale factors and side lengths of one of the similar triangles. In similar triangles, corresponding proportion. Find x x Corollary to the Side Splitter If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. Sheet 1. 4 with 8, and so the ratio of sides in triangle S to triangle R is 6. Name Score Printable Math Worksheets www. The smallest side of the first triangle corresponds to the smallest. t Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name Similar Triangles Date Period State if the triangles in each pair are similar. Sketching Similar Triangles Rally Coach worksheet Similar Triangles-Finding Missing. Similar Figures. Materials Overhead of figures for the Similarity Basketball Game Trash can or box for basketball goal, and a foam ball Masking tape for shooting line. To calculate a missing length, draw the two triangles separately and label the lengths. com t t t t K L M t t t A B C. 5 cm 22 cm 16. small small big big The missing side is . Math 7. Trigonometry allows us to find sides of triangles that we would not normally be able to find, by taking advantage of the sine, cosine, and tangent ratios. Sheet 1. Similar Figures - Polygons that have the same shape, but different size. If so, state how you know they are similar and complete the. X ,y 5. Displaying all worksheets related to - Finding A Missing Side In Similar Figures. This property can be written as follows dfrac a a' dfrac b b' dfrac c c' s aa bb cc s where a, b, c - sides lengths of the first triangle, a', b', c' - sides lengths of the second triangle,. A MEDIAN of a triangle is a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side An ALTITUDE of a triangle is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. P SIM 07 HW63b State if the triangles in each pair are similar. 110 Ratings. Finding Missing Angles Worksheet (With Answers And Pdf) Finding Missing Angles Step 1 Find the missing angle in an isosceles triangle Step 2 The sum of the measure of the three interior angles of a triangle is always 180&176;. L Worksheet by Kuta Software LLC Geometry ID 1. Recall the three main trigonometric functions. For 5-8, side c is the hypotenuse of the. If so, state how you know they are similar and complete the. L Worksheet by Kuta Software LLC Geometry ID 1 Name Date Period e G2t0 s1N3T pK Ou4t war WShoTf vtqw9aIr Be k cL ALlC j. Find the missing angle in each triangle. Find the missing side. A similar triangle has sides measuring x cm, 24 cm, and 24 cm. To find a missing side length set up and solve a . J A M h 1 D E B h 2 60 126 40 68 18. Round your answer to the nearest tenth. 5 Google Classroom Solve for x x. The smallest side of the first triangle corresponds to the smallest. Solve real-life problems involving similar triangles. Sheet 1. 9 62G0j1 Y2K iK XuutXaj aSEobf ft lwCasrAet cLIL OCI. a) Find the missing angle in each triangle. The worth of tan inverse 1 is equal to 4 rad by means of pi. (No printing, cutting, laminating, or grading). They find missing side lengths of similar polygons, triangles, and other shapes. If so, state how you know they are similar and complete the similarity statement. com t t t t K L M t t t A B C. Materials Overhead of figures for the Similarity Basketball Game Trash can or box for basketball goal, and a foam ball Masking tape for shooting line. Identify triangles as similar or not and use proportions to finding missing lengths of similar triangles. Find the missing side and angle. Answers to Practice Ch. The smallest side of the first triangle corresponds to the smallest. Try the free Mathway calculator and problem solver below to practice various math topics. This activity sheet, containing twenty exercises, has students working with the concept that if two polygons are similar then their corresponding angles are congruent and their corresponding sides are proportional. T Worksheet by Kuta Software LLC. 7) similar; SSS similarity; QRS8) not similar Find the missing length. Solve each proportion. I can use proportions in similar triangles to solve for missing sides. Similar Triangles - Missing. Worksheet by Kuta Software LLC. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. Steps to find a missing measurement 1) Determine the corresponding sides 2) Set up a proportion 3) Cross multiply to solve for the missing length 4) Label your answer and check your work 1. E p 6A 6l zl w IrHiJg ahDt7s c 5r Mevsmelr 3vhe Udj. If so, state how you know they are similar and complete the. Which of the following proportions is true for these. Sketching Similar Triangles Rally Coach worksheet Similar Triangles-Finding Missing. 4 in Triangle S The 6. Identifying Similar Triangles Identify the similar triangles in the diagram. We divide it by 2, to get the length of each unknown side. 4 Y kARl Ml3 Xr LiBgrh atJsZ Tr MeZs te crDv he Ld L. 9 10 B A C 5) 7. Materials Overhead of figures for the Similarity Basketball Game Trash can or box for basketball goal, and a foam ball Masking tape for shooting line. Identifying Similar Triangles When the altitude is drawn to the hypotenuse of a right triangle, the two smaller triangles are similar to the original triangle and to each other. Steps to find a missing measurement 1) Determine the corresponding sides 2) Set up a proportion 3) Cross multiply to solve for the missing length 4) Label your answer and check your work 1. You may select whether to include non-similar triangle pairs, as well as the. Examples, videos, worksheets, and solutions to help Grade 8 students learn how to find missing sides and angles of similar triangles. Now, we subtract the sum we got from the total perimeter. Similar Figures. Step 1 Given a pair of similar triangles, determine which sides correspond to each other. The smallest side of the first triangle corresponds to the smallest. How to set up and find the missing side in a triangle. All angles in similar figures are congruent. Solve real-life problems involving similar triangles. How to find a missing length in a triangle · Use angle facts to determine which angles are equal. Similarity, Congruence and Transformations Similarity in Triangles Worksheet Shapes and Figures Similar Triangles (1 of 2) e. After solving for x, they should find the length of the missing side and find the card with the correct answer. The triangles in each pair are similar. Similar Figures Worksheet Name Show All Work Where Necessary You can use proportional relationships to find missing side lengths in similar figures Solve each proportion. ) Sam wants to enlarge a triangle with sides 3, 6 and 6 inches. 5 Google Classroom Solve for x x. Tags 5th Grade 6th Grade. Students use the properties of similar triangles to find the missing side . Students practice finding missing segment lengths in in similar right triangles in this matching activity to use in a variety of ways. If so, state how you know they are similar and complete the. Right Triangle Trig. P SIM 07 HW63b State if the triangles in each pair are similar. 5 Similar Triangle Applications - Rochester City School District. 11-6 - Find Missing Side - Similar Triangles. Similar Figures - Polygons that have the same shape, but different size. Identify triangles as similar or not and use proportions to finding missing lengths of similar triangles. For Exercises 18 and 19, use the triangles shown below. Materials Overhead of figures for the Similarity Basketball Game Trash can or box for basketball goal, and a foam ball Masking tape for shooting line. ALMN , Find the length of IJ and then the length of 1K. Clear up math equations. Similar Figures Worksheet. Offered in this set of pdf worksheets are the scale factors and side lengths of one of the similar triangles. Some of the worksheets displayed are Similar triangle work, Similar figures date period, Similar triangles, Solving proportions involving similar figures, Similar triangles date period, Work similar triangles, Name period gl unit 5 similarity, Geometry. Find the missing The triangles in each pair are similar. Students use the properties of similar triangles to find the missing side . These Similarity Worksheets will produce eight problems for working with similar triangles. 11-6 - Find Missing Side - Similar Triangles. We compare the ratios and find the length of the unknown side of the triangle. Kuta Software - Infinite Geometry Similar Right Triangles Name Date Period Find the missing length indicated. a) Find the missing side lengths. If so, state how you know they are similar and complete the. Sketching Similar Triangles Rally Coach worksheet Similar Triangles-Finding Missing. We simply need to add ABC180&176; AB80&176; 180&176; - 80&176;C100&176; C angle will be 100&176;. 00 PDF This quiz assesses how well students can find the missing side length of a shape when given a another shape that is similar. literoctia stories, valorant unban appeal
11-6 - Find Missing Side - Similar Triangles. . Similar triangles find missing side worksheet
Place the 10 cards on the wall around your room. Similar Figures. Worksheet by Kuta Software LLC Practice Ch. Activity 1. I can set up and solve problems using properties of similar triangles. b) Find the ratio of the perimeter of JAM to the perimeter of DEB. Therefore, we can write a proportion to find the missing side . Let&x27;s restate the sine, cosine, and tangent ratios before we start on examples Definition Let be one of the acute angles of a right triangle. 0 Worksheet by Kuta Software LLC Algebra 1 - Mr. The smallest side of the first triangle corresponds to the smallest. If so, state how you know they are similar and complete the. Find the missing measurement. Worksheet by Kuta Software LLC Practice Ch. 15 c. Similar Figures. t Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name Similar Triangles Date Period State if the triangles in each pair are similar. 2) Find the area of square of side a) 27cm. ID 11 Practice Ch. The set includes 18 pairs of matching cards (18 problems of all types)one side with diagram of triangles, the other side a segment measure. How does this show that the triangles are similar Deal with mathematic question Mathematics is a powerful tool that can be used to solve problems in a variety of fields. Activity 1. Answers to Practice Ch. 8 F 4MNaRd AeT awJiXtkh S KIZn AfVinfi Pt DeJ wGIe Ro9m1eZtGrTy5. To learn about the different types of angles, use a worksheet that identifies the vertex and the arms. Eraser Highlighter - blue. Great for a quick check to . Find the Sides of the Triangles using the Scale Factor. Similar Triangles Worksheets. For the following exercises, remedy for the unknown sides of the. Find the missing length. Similar Triangles - Missing. This set of Boom Cards features 40 different Digital Self-Checking Task Cards. Step 1 Given a pair of similar triangles, determine which sides correspond to each other. Sheet 1. 11-6 - Find Missing Side - Similar Triangles. 12 in 8 in 18 in 18 in d d d d t t t Similar Triangles - Missing SidesT1S1 Name Printable Worksheets www. M p PAsl l0 qr hiUgjhWtTs 2 CrmexsUeDrsv deOdn. 6) The perimeter of a room is 16cmand breadth. Similar Figures. 9 meter high. What is x answer choices x 19 cm x 24 cm x 3 cm x 16. Similar Triangles - Missing. 4 Y kARl Ml3 Xr LiBgrh atJsZ Tr MeZs te crDv he Ld L. T Worksheet by Kuta Software LLC. If so, state how you know they are similar and complete the similarity statement. - Finding Missing Sides and AnglesDate Period Find the measure of each angle indicated. Let&39;s find missing side lengths in triangles. Find the missing measurement. 0 Worksheet by Kuta Software LLC Algebra 1 - Mr. 11-6 - Find Missing Side - Similar Triangles. Find the missing The triangles in each pair are similar. Similar Figures - Polygons that have the same shape, but different size. x Practice Problems Find the missing side(s) in each similar figure. Steps to determine if two figures are similar 1) Take the first set of corresponding sides and write them as the first fraction of the proportion. In the process students are reviewing the concepts of ratio, scale, factors and proportion. How to Find the Missing Sides of Similar Triangles. When the lengths of all sides of a triangle are added, the result is called the perimeter of the triangle. Identify triangles as similar or not and use proportions to finding missing lengths of similar triangles. Steps to determine if two figures are similar 1) Take the first set of corresponding sides and write them as the first fraction of the proportion. For Exercises 18 and 19, use the triangles shown below. How do you find the missing side of a similar triangle · Find the scale factor k of the similar triangles by taking the ratio of any known side . Each pair of figures is similar. I can prove triangles are congruent in a two-column proof. Algebra 1 - Mr. Find the missing length. How to Find the Missing Sides of Similar Triangles. Find the Sides of the Triangles using the Scale Factor. When one of the similar triangles has a side that is missing, we will find it. Find the missing side length x. Students practice finding missing segment lengths in in similar right triangles in this matching activity to use in a variety of ways. Sheet 1. b) 17cm. 8 F 4MNaRd AeT awJiXtkh S KIZn AfVinfi Pt DeJ wGIe Ro9m1eZtGrTy5. Find missing lengths in similar shapes which have sides overlapping Find missing lengths in similar shapes which have sides overlapping In this lesson, we will find missing side lengths for similar shapes which have side lengths overlapping Back Start Lesson. Triangles are strong because of their inherent structural characteristics. Similar Figures. Persons 1 does problem 1. Put the measurements of the smaller figure on top and the bigger figure on the bottom. Chapter 11. find the missing measurements of two similar figures. Similar Figures. 4 Y kARl Ml3 Xr LiBgrh atJsZ Tr MeZs te crDv he Ld L. com t t t t K L M t t t A B C. Question 1 Shapes P P and Q Q are mathematically similar. Find its perimeter and area. So we can match 6. Solve similar triangles (basic) Solving similar triangles same side plays different roles Solve similar triangles (advanced) Math > High school geometry > Similarity > Solving similar triangles 2023 Khan Academy Terms of use Privacy Policy Cookie Notice Solve similar triangles (advanced) CCSS. Similar triangles worksheet Subject Mathematics Age range 14-16 Resource type WorksheetActivity 24 reviews File previews pptx, 334. Practice Ch. You may select equilateral, right scalene, right isosceles, obtuse scalene, obtuse isosceles, acute scalene and acute isosceles. If so, state how you know they are similar and complete the. Similar Figures Worksheet Name Show All Work Where Necessary You can use proportional relationships to find missing side lengths in similar figures Solve each proportion. 5 cm. Sketching Similar Triangles Rally Coach worksheet Similar Triangles-Finding Missing. Finding Missing Sides - Algebraic Similar Triangle Practice ID 1742104 Language English School subject Math Gradelevel 9-12 Age 13-18 Main content Triangles Other contents Add to my workbooks (2) Download file pdf Embed in my website or blog Add to Google Classroom Add to Microsoft Teams Share through Whatsapp Link to this worksheet Copy. Find the measure of each angle 746 Teachers 9. Math HSG. To calculate a missing length, draw the two triangles separately and label the lengths. Name Score Printable Math Worksheets www. Now we know that the height of Rectangle B is. Page 2. Similar Figures Worksheet Name Show All Work Where Necessary You can use proportional relationships to find missing side lengths in similar figures Solve each proportion. (4) The two smaller triangles, ADC and BDC, are similar. Triangles online worksheet for 9-12. E p 6A 6l zl w IrHiJg ahDt7s c 5r Mevsmelr 3vhe Udj. Solve each proportion. How to find a missing length in a triangle. 2 in 6. 2 2 4. Similar Triangle Missing Side Worksheets - total of 8 printable worksheets available for this concept. PYTHAGOREAN THEOREM - WORKSHEET. 42 If a 36-inch yardstick casts a 21 -foot shadow, how tall is a building whose shadow is 168 feet (Draw a picture with two similar polygons. How to Find the Missing Sides of Similar Triangles. The triangles in each pair are similar. Identifying Similar Triangles Identify the similar triangles in the diagram. Worksheet by Kuta Software LLC. Triangles online worksheet for 9-12. Find the Sides of the Triangles using the Scale Factor. 11-6 - Find Missing Side - Similar Triangles. Finding Missing Sides Of Similar Triangles Activity Similar Figures - Polygons that have the same shape, but different size. Find the missing length. T Worksheet by Kuta Software LLC. Let&x27;s restate the sine, cosine, and tangent ratios before we start on examples Definition Let be one of the acute angles of a right triangle. How does this show that the triangles are similar Deal with mathematic question Mathematics is a powerful tool that can be used to solve problems in a variety of fields. Similar Triangles - Missing Sides T1S1 Name Printable Worksheets www. Finding Missing Sides of Triangles Worksheet. Identifying Similar Triangles When the altitude is drawn to the hypotenuse of a right triangle, the two smaller triangles are similar to the original triangle and to each other. . spypoint