Section 6.4 Notes. If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. If  K   Y and.

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Presentation transcript:

Section 6.4 Notes

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. If  K   Y and  J   X, then ΔJKL ~ ΔXYZ. Angle-Angle (AA) Similarity Postulate

Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. Example 1

B  EB  E since all right angles are congruent. m  A + m  C = 90° so m  A = 22°. m  A = m  D so by the definition of congruent angles  A   D. Therefore ΔABC ~ ΔDEF by the AA Similarity Post.

Determine whether the triangles are similar. If they are, write a similarity statement. Explain your reasoning. Example 2

B  YB  Y since all right angles are congruent. m  A + m  C = 90° so m  A = 53°. m  A = m  X so by the definition of congruent angles  A   X. Therefore ΔABC ~ ΔXYZ by the AA Similarity Post.

Given:  DFE   EBC Prove: ΔDEF ~ ΔCEB Example 3 B C F E D

StatementsReasons 1.  DFE   EBC 1. Given 2.  DEF   BEC2. Vert.  s Thm. 3. ΔDEF ~ ΔCEB3. AA Similarity Post.

Given: seg. AB | | seg. DE Prove: ΔABC ~ ΔEDC Example 4 E D C B A

StatementsReasons 1. seg. AB | | seg. DE1. Given 2.  D   B2. Alt. Int.  s Thm. 3.  DCE  ΔBCA3. Vert.  s Thm. 4. ΔABC ~ ΔEDC4. AA Similarity Post.

A lifeguard is standing beside the lifeguard chair on a beach. The lifeguard is 6 feet 4 inches tall and casts a shadow that is 48 inches long. The chair casts a shadow that is 6 feet long. How tall is the chair? Example 5

lifeguard 76 inches shadow 48 inches lifeguard chair shadow 6 ft. The lifeguard chair is 9.5 ft. tall.

A school building casts a shadow that is 26 feet long. At the same time a student standing nearby, who is 71 inches tall, casts a shadow that is 48 inches long. How tall is the building? Example 6

boy 71 inches shadow 48 inches building shadow 26 ft.