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TOPIC 9-4: SIMILAR TRIANGLES When polygons are similar, two criteria must be met: 1) Corresponding angles are ____________________. 2) Corresponding sides are ___________________________. However…if you don’t know the measures of all sides and angles, is there another way to tell? There are several theorems that allow us to show that triangles are similar. AA ________________-________________ Similarity If two angles of one triangle are _____________ to two angles of another triangle, then the Similarity triangles are _________________. EXAMPLE 1 Can these triangles be proven similar by AA? If so, write a similarity statement. G A a) b) J H C E F K B YES or NO D ____________________ YES or NO ___________________ You can use AA Similarity to find missing measurements in triangles. EXAMPLE 2 Given AB CD, AB = 4, AE = 3x + 1, CD = 8, and ED = x + 12, find AE and DE. A C E B D A second way to show that triangles are similar is: ________________-________________ -_____________ Similarity In two triangles, if a pair of corresponding angles is SAS _______ and the sides including the angle are Similarity __________________________, then the triangles are ______________________. EXAMPLE 3 Can the two triangles be proven similar by SAS? If so, write a similarity statement. Q L 9 6 M 4 120 N P YES or 6 NO ___________ ___________ 120 R There is a third way to show that triangles are similar… ________________-________________ -_____________ Similarity SSS If all three pairs of corresponding sides of two triangles are _______________________, then Similarity the two triangles are _____________________. EXAMPLE 4 Are the triangles below similar by SSS? If so, write a similarity statement. X S T 9 4 3 U 5 12 W YES or V 15 NO ___________ ___________ EXAMPLE 5 Are the two triangles similar? If so, state how and write a similarity statement. X 5. 6. 7. L E W 80 V K 80 YES Y or NO HOW? _________________ 6 6 F G M 3 Z 5 3 10 6 D 5 10 6 N J H YES or NO HOW? _________________ YES or NO HOW? _________________ EXAMPLE 6 Solve for ‘x’ and for ‘y’. A x B 8 y E 3 D 3 4 C EXAMPLE 7 Are the two triangles similar, and if so what is the common ratio? a. The measures of the sides of ABC are 4, 5, & 7. The measures of XYZ are 16, 20, & 28. b. PQR has sides 3, 5, & 6. STU has sides 2.5, 2, & 3.