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5.3 Proving Triangle Similar

5.3 Proving Triangle Similar. Postulate 15: If the three angles of one triangle are congruent to the three angles of a second triangle, then the triangles are similar (AAA)

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5.3 Proving Triangle Similar

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  1. 5.3 Proving Triangle Similar • Postulate 15: If the three angles of one triangle are congruent to the three angles of a second triangle, then the triangles are similar (AAA) • Corollary 5.3.1: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar (AA) • CSSTP: Corresponding sides of similar triangles are proportional • CASTC: Corresponding angles of similar triangles are congruent. Example 2 p. 234 Section 5.3 Nack

  2. Theorem 5.3.2: The lengths of the corresponding altitudes of similar triangles have the same ratio as the lengths of any pair of corresponding sides. Theorem 5.3.3 (SAS~): If an angle of one triangle is congruent to an angle of a second triangle and the pairs of sides including the angles are proportional, then the triangles are similar. Theorem 5.3.4 (SSS~): If the three sides of one triangle are proportional to the three corresponding sides of a second triangle, then the triangles are similar. Example 5 p. 236 Section 5.3 Nack

  3. Dividing Sides Proportionally • Lemma 5.3.5: If a line segment divides two sides of a triangle proportionally, then this line segment is parallel to the third side of the triangle. Proof p. 237 • Using Lemma 5.3.5 to prove SAS~ p. 237 Section 5.3 Nack

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