9-3: Similar Triangles.

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Presentation transcript:

9-3: Similar Triangles

9-3: Similar Triangles Back in Chapter 5, we talked postulates for triangle congruence SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side) The only two triangle congruence statements that didn’t work were AAA and ASS. When talking about similarity, one of them does work

9-3: Similar Triangles AA Similarity: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. The rest of our postulates can be applied for similarity SSS Similarity SAS Similarity ASA Similarity & AAS Similarity fall under AA Similarity

9-3: Similar Triangles Example #1 Determine whether the two triangles are similar. If so, tell which similarity test is used and complete the statement. GHK ~ _____ JMP Because 6/9 = 10/15 = 14/21 These triangles have SSS Similarity

9-3: Similar Triangles Example #2 Find the value of x Sometimes, it helps to rotate/flip an image to better see how the parts correspond. 9/3 = x/5 3x = 45 x = 15 9 12

9-3: Similar Triangles Your Turn Determine if the triangles are similar. If so, tell which similarity test and complete the statement DGH ~ _____ Not similar

9-3: Similar Triangles Your Turn #2 Find the values of x and y if the triangles are similar. x = 36 y = 39

9-3: Similar Triangles Similar Triangles can be used to measure things that otherwise could prove to be difficult. Example: A tree casts a shadow of 18 feet long. If you are 6 feet tall and cast a 4 foot shadow, how tall is the tree? DRAW A DIAGRAM!!! (next slide)

9-3: Similar Triangles 6/4 = x/18 108 = 4x 27 = x

9-3: Similar Triangles Assignment Worksheet #9-3