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Understanding Triangle Similarity with AA Postulate

Learn to show triangles are similar using AA Similarity Postulate and solve problems involving angle congruence to determine similarity. Practice with examples and checkpoints.

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Understanding Triangle Similarity with AA Postulate

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  1. 7.3 OBJ: Show that two triangles are similar using the AA Similarity Postulate EQ: How do you show 2 triangles are similar?

  2. Angle-Angle (AA) Similarity Postulate • If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

  3. Determine whether the triangles are similar. If they are similar, write a similarity statement. Explain your reasoning. SOLUTION If two pairs of angles are congruent, then the triangles are similar. G  Lbecause they are both marked as right angles. 1. Example 1 Use the AA Similarity Postulate

  4. mF + 90°+ 61°= 180° Triangle Sum Theorem mF + 151° = 180° Add. Subtract 151° from each side. mF = 29° By the AA Similarity Postulate,FGH~ JLK ANSWER Find mFto determine whether Fis congruent to J. 2. Example 1 Use the AA Similarity Postulate Both Fand Jmeasure 29°, so F J.

  5. Are you given enough information to show that RST is similar to RUV? Explain your reasoning. SOLUTION Redraw the diagram as two triangles: RUVand RST. Example 2 Use the AA Similarity Postulate RSTRUV. RRby the Reflexive Property of Congruence. Using AA Similarity Postulate, RST~RUV.

  6. Checkpoint Determine whether the triangles are similar. If they are similar, write a similarity statement. 1. Use the AA Similarity Postulate

  7. Checkpoint Determine whether the triangles are similar. If they are similar, write a similarity statement. 1. Use the AA Similarity Postulate

  8. Checkpoint 2. yes; GLH~GKJ ANSWER Use the AA Similarity Postulate Determine whether the triangles are similar. If they are similar, write a similarity statement.

  9. Checkpoint Write a similarity statement for the triangles. Then find the value of the variable. 3. Use Similar Triangles

  10. Checkpoint Write a similarity statement for the triangles. Then find the value of the variable. 3. Use Similar Triangles 5 = 15 3 y 5y = 3(15) 5y = 45 Y = 9

  11. Homework • Worksheet 7.3A • Quiz 7.1-7.3

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