Geom Notes 7 Triangles are Similar

Geometry 7.3: Showing Triangles are Similar: AA Name: Angle-Angle Similarity Postulate (AA): If two angles of one triangle are congruent to two angles of another triangle, then   the two triangles are similar. If ∠A ≅ ∠X and ∠B ≅ ∠Y, then ∆ABC ~ ∆XYZ. Example 1: Determine whether the triangles are similar. If they are similar, write a similarity statement and explain. a. ∆HGF ~ ∆KLS by AA. b. Not similar. Example 2: Are you given enough information to show that ∆RST is similar to ∆RUV? Explain. Yes, ∆RST ~ ∆RUV by AA. Example 3: A hockey player passes the puck to a teammate by bouncing the puck off the wall of the rink, as shown below. According to the laws of physics, the angles that the path of the puck makes with the wall are congruent. How far from   the wall will the teammate pick up the pass?   25/x = 40/28 40x = 700 x = 17.5 ft hockey rink with a puck bouncing off the wall Example 4: Write a similarity statement for the triangles. Then find the value of x. a. ΔMNP ~ ΔRST 16/x = 20/15 20x = 240 x = 12 two triangles, MNP and RST b. ΔJKL ~ ΔCDE 9/6 = 15/x 9x = 90 x = 10 two triangles YOU TRY: Find the value of the variable. 5/15 = 15/y two triangles, FGH and XYZ Example 5: Use the diagram to complete the statements. a. ΔFGH ~ ΔXYZ b. FH/XZ = GH/YZ c. Find the value of x. x/15 = 6/10 6x = 90 x = 15 c. Find the scale factor of ΔXYZ to ΔFGH. 6/15 = 2/5 two triangles YOU Try: Determine whether the triangles are similar. If they are similar, write a similarity statement. 1. ΔGLH ~ ΔGJK 2. Not similar 3. ΔWVX ~ ΔZYX