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9-3: Similar Triangles

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.

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9-3: Similar Triangles

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  1. 9-3: Similar Triangles

  2. 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

  3. 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

  4. 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 Because6/9 = 10/15 = 14/21These triangles have SSSSimilarity

  5. 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

  6. 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

  7. 9-3: Similar Triangles • Your Turn #2 • Find the values of x and y if the triangles are similar. • x = 36 • y = 39

  8. 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. 9-3: Similar Triangles • 6/4 = x/18 • 108 = 4x • 27 = x

  10. 9-3: Similar Triangles • Assignment • Worksheet #9-3

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