Course: Applied Geo. Aim: Similar Triangles Aim: What is special about similar triangles? Do Now: In the diagram at right  PQR ~  STU. Name the pairs.

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Course: Applied Geo. Aim: Similar Triangles Aim: What is special about similar triangles? Do Now: In the diagram at right  PQR ~  STU. Name the pairs of corresponding angles: Q & T R & U P & S

Course: Applied Geo. Aim: Similar Triangles In the diagram at right  PQR ~  STU. A. Name the pairs of corresponding angles: Q & T R & U P & S B. Name the pairs of corresponding sides: PQ & ST QR & TU PR & SU C. Find the ratio of similitude between PQR and STU. D. Find the value of y. E. Find the value of x. Problem #1 QR TU = = 3 2 = 12 y 3y = 24 y = = 9 x 3x = 18 x = 6 Short cuts, anyone?

Course: Applied Geo. Aim: Similar Triangles Similar Triangles Theorem 1: If the corresponding sides of two triangles are in proportion, the triangles are similar. Theorem 1: If the corresponding sides of two triangles are in proportion, the triangles are similar. Note: this is only true for triangles!! Theorem 2: If two angles of one triangle are congruent to two angles of a second triangle, then the two triangles are similar. Two triangles are similar if AA Theorem 2: If two angles of one triangle are congruent to two angles of a second triangle, then the two triangles are similar. Two triangles are similar if AA Short cuts, anyone?

Course: Applied Geo. Aim: Similar Triangles a.Explain why the two triangles are similar b. Name the three pair of corresponding sides. A B C W M E AA AB & EM, BC & MW, AC & EW c. Name the three pair of corresponding angles.  A &  E,  B &  M,  C &  W Model Problem

Course: Applied Geo. Aim: Similar Triangles Determine if the two triangles are similar. 1.3 in 0.8 in Q 1.9 in P R H 0.4 in G 1.0 in 0.7 in I Since no angles are given we must determine if the sides are in proportion. Because we have shown that two sides of the triangles are not in proportion, it is enough then, to state that they are not similar. Model Problem

Course: Applied Geo. Aim: Similar Triangles Explain why the triangles are similar R V B S W 45 0  WSR   VSB because vertical angles are congruent  R   V because their measures are equal  RSW   VSB because triangles are similar is two angles of the triangles are congruent AA  AA Model Problem

Course: Applied Geo. Aim: Similar Triangles x m. 6 m. 3 m. The lengths, in meters, of the sides of a triangle are 24, 20, and 12. If the longest sides of a similar triangle is 6 meters, what is the length of the shortest side? 24 m. 20 m. 12 m. 2. Because they are similar, corresponding sides are in proportion 1. Draw a picture 24x = (6)(12) = 72 x = 3 Model Problem

Course: Applied Geo. Aim: Similar Triangles PJ is 6-ft. tall. He casts a shadow that is four feet long. A nearby tree of unknown height casts a shadow of 30 feet. How tall is the tree? PJ’s ht. 6 ft. PJ’s shadow - 4 ft. Tree Height x Tree’s shadow 30 ft. x = 45 feet 45 11 22  1 ~  2