Proportions and Similarity Similar Triangles

Similar Triangles You will learn to use AA, SSS, and SAS similarity tests for triangles.

Similar Triangles 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. Some of the triangles are similar, as shown below.

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 A B F E D If A ≈ D and B ≈ E, then ΔABC ~ ΔDEF

Similar Triangles Two other tests are used to determine whether two triangles are similar. proportional C A B F E D 1 2 3 6 4 8 then the triangles are similar then ΔABC ~ ΔDEF

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

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

Similar Triangles Fransisco needs to know the tree’s height. The tree’s shadow is 18 feet long at 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 ft. 4 ft. 18 ft. 4 18 6 t 4t = 108 t = 27 The tree is 27 feet tall!

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

Similar Triangles