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Similar Polygons

Vocabulary. Similar Polygons. What You'll Learn. You will learn to identify similar polygons. 1) polygons 2) sides 3) similar polygons 4) scale drawing. D. Δ ABC is similar to Δ DEF. A. C. B. F. E. Similar Polygons.

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Similar Polygons

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  1. Vocabulary Similar Polygons What You'll Learn You will learn to identify similar polygons. 1) polygons 2) sides 3) similar polygons 4) scale drawing

  2. D ΔABC is similar toΔDEF A C B F E Similar Polygons A polygon is a ______ figure in a plane formed by segments called sides. closed It is a general term used to describe a geometric figure with at least three sides. Polygons that are the same shape but not necessarily the same size are called ______________. similar polygons The symbol ~ is used to show that two figures are similar. ΔABC ~ ΔDEF

  3. and D C G H E F A B Similar Polygons proportional Polygon ABCD~ polygon EFGH

  4. Guided Practice pg. 373 #1 List all pairs of congruent angles. Write the ratios of the corresponding side lengths in a statement of proportionality.

  5. 6 4 5 7 5 7 4 6 = Similar Polygons Determine if the polygons are similar. Justify your answer. 6 4 5 7 1) Are corresponding angles are _________. congruent 2) Are corresponding sides ___________. proportional 0.66 = 0.71 The polygons are NOT similar!

  6. R 5 Write the proportion thatcan be solved for y. 4 J S T 6 x = 7 Write the proportion thatcan be solved for x. = K L y + 2 Similar Polygons Find the values of x and y if ΔRST ~ ΔJKL 6 4 y + 2 7 4(y + 2) = 42 4y + 8 = 42 5 4 4y = 34 x 7 4x = 35

  7. A 5 3 C B 7 CA BC AB = = FD EF DE D or 7 5 3 = = 10 6 6 14 10 1 2 1 2 2 1 E F 14 Similarity The ratio found by comparing the measures of corresponding sides of similar triangles is called the constant of proportionality or the ___________. scale factor If ΔABC ~ ΔDEF, then The scale factor of ΔABC to ΔDEF is Each ratio is equivalent to The scale factor of ΔDEF to ΔABC is

  8. Guided Practice #2, and 3 pg. 373 2. What is the scale factor of QRST to ABCD? 3. Find the value of x.

  9. D A C B F E perimeter of ΔABC CA AB BC = = = FD perimeter of ΔDEF DE EF Perimeters and Similarity the measures of the corresponding perimeters are proportional to the measures of the corresponding sides. If ΔABC ~ ΔDEF, then

  10. M 4.5 R z 3 T P x 6 Y N S perimeter of ΔMNP NP PM MN MN MN = = = ST TR RS RS RS perimeter of ΔRST 6 4.5 3 3 13.5 3 = = = y z 2 2 x 9 y = 4 x = 2 z = 3 Perimeters and Similarity The perimeter of ΔRST is 9 units, and ΔRST ~ ΔMNP. Find the value of each variable. Theorem 9-10 The perimeter of ΔMNP is 3 + 6 + 4.5 3y = 12 3z = 9 27 = 13.5x Cross Products

  11. Vocabulary Similar Triangles What You'll Learn You will learn to use AA similarity tests for triangles. Nothing New!

  12. Similar Triangles Some of the triangles are similar, as shown below. The Bank of China building in Hong Kong is one of the ten tallest buildings in the world. Designed by American architect I.M. Pei, the outside of the 70-story building is sectioned into triangles which are meant to resemble the trunk of a bamboo plant.

  13. Similar Triangles In previous lessons, you learned several basic tests for determining whether two triangles are congruent. Recall that each congruence test involves only three corresponding parts of each triangle. Likewise, there are tests for similarity that will not involve all the parts of each triangle. similar C F D E A B If A ≈ D and B ≈ E, then ΔABC ~ ΔDEF

  14. = Similar Triangles Fransisco needs to know the tree’s height. The tree’s shadow is 18 feet longat the same time that his shadow is 4 feet long. If Fransisco is 6 feet tall, how tall is the tree? 1) The sun’s rays form congruent angles with the ground. 2) Both Fransisco and the tree form right angles with the ground. 6 4 t 18 4t= 108 t= 27 6 ft. The tree is 27 feet tall! 4 ft. 18 ft.

  15. 45 m x 8 m 10 m Similar Triangles Slade is a surveyor. To find the distance across Muddy Pond, he forms similar triangles and measures distances as shown. What is the distance across Muddy Pond? 10 8 = It is 36 meters across Muddy Pond! x 45 10x = 360 x = 36

  16. Guided Practice # 2 Read the directions and draw the diagram before you determine if the triangles are similar Solution: Angle CDF is 58 degrees ( congruent to angle DEF) Angle DFC is congruent to Angle 90 degrees Angle DFE is congruent to Angle 90 degrees Since two corresponding angles are congruent then the triangles are similar.

  17. Similar Triangles Two other tests are used to determine whether two triangles are similar. C F 2 1 A E D B 4 8 and Angle A is congruent to Angle D then the triangles are similar

  18. Similar Triangles proportional C F 2 1 D A E B 4 8 then ΔABC ~ ΔDEF

  19. J 14 G K 9 21 6 10 H M 15 P Similar Triangles Determine whether the triangles are similar. If so, tell which similarity test is used and complete the statement. 6 10 14 , the triangles are similar by SSS similarity. Since = = 15 21 9 JMP Therefore, ΔGHK ~Δ

  20. Guided Practice #3,4 Please read the directions and draw the triangles on your paper to help you out. #3 Solution: <R < N and therefore the triangles are similar by the SAS Similarity Theorem. #4 Solution: <WZX <XZY and therefore the triangles are similar by either SSS or SAS Similarity Theorem.

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