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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) Ex. 1 p.236 Section 5.3 Nack

  2. Proving Triangle Similar (cont.) • CSSTP: Corresponding sides of similar triangles are proportional • CASTC: Corresponding angles of similar triangles are congruent. • Example 2, 3 p. 236-7 • 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. • Ex. 4 p. 238 Section 5.3 Nack

  3. Theorem 5.3.2: Then lengths of the corresponding altitudes of similar triangles have the same ratio as the lengths of any pair of corresponding sides. 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. 238 Section 5.3 Nack

  4. 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. 239 • Using Lemma 5.3.5 to prove SAS~ p. 239 Section 5.3 Nack

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