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Section 6.4 AA Similarity

Section 6.4 AA Similarity. Review Triangle Angle Sum Theorem Three angles in a triangle have a sum of ______ Similar Figures Angles are _________, sides are ______________. So… if two angles of a triangle are 90 ° and 40 ° , what is the measure of the third angle?

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Section 6.4 AA Similarity

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  1. Section 6.4 AA Similarity • Review • Triangle Angle Sum Theorem • Three angles in a triangle have a sum of ______ • Similar Figures • Angles are _________, sides are ______________

  2. So… if two angles of a triangle are 90° and 40°, what is the measure of the third angle? • If two angles of another triangle are 90° and 40°, what is the measure of it’s third angle? • What do you know about the two triangles?

  3. They are SIMILAR triangles since all three angles are congruent. • Do you always need to know the measure of the third angle to know if the triangles are similar?

  4. Angle Angle (AA) Similarity Theorem • If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. • You can then write a similarity statement for the two triangles.

  5. Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. EXAMPLE 1 Use the AA Similarity Postulate

  6. b. a. ∆ABEand ∆ACD ∆SVRand ∆UVT EXAMPLE 2 Show that triangles are similar Show that the two triangles are similar.

  7. 1. ∆FGHand ∆RQS ANSWER In each triangle all three angles measure 60°, so by the AA similarity postulate, the triangles are similar ∆FGH ~ ∆QRS. for Examples 1 and 2 GUIDED PRACTICE Show that the triangles are similar. Write a similarity statement.

  8. 2. ∆CDFand ∆DEF ANSWER Since m CDF = 58° by the Triangle Sum Theorem and mDFE = 90° by the Linear Pair Postulate the two triangles are similar by theAASimilarity Postulate; ∆CDF ~ ∆DEF. for Examples 1 and 2 GUIDED PRACTICE Show that the triangles are similar. Write a similarity statement.

  9. EXAMPLE 3 Standardized Test Practice

  10. 4. Achild who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow? (The woman is 5 feet four inches tall and her shadow is 40 inches long.) 36.25 in. ANSWER for Example 3 GUIDED PRACTICE

  11. 5. You are standing in your backyard, and you measure the lengths of the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree. SAMPLE ANSWER length of shadow tree height = length of your shadow your height for Example 3 GUIDED PRACTICE

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