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Proving Triangles Congruent ASA and AAS

Proving Triangles Congruent ASA and AAS. Investigation Is ASA a congruence shortcut? Step 1: Construct a triangle with angles of 30° and 45° at each end of a segment with a length of 3 inches Step 2: Compare your triangle to those around you. Are they congruent?

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Proving Triangles Congruent ASA and AAS

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  1. Proving Triangles Congruent ASA and AAS Investigation Is ASA a congruence shortcut? • Step 1: • Construct a triangle with angles of 30° and 45° at each end of a segment with a length of 3 inches • Step 2: • Compare your triangle to those around you. Are they congruent? Postulate 14 Angle-Side-Angle Congruence Postulate (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, thenthe two triangles are congruent.

  2. Proving Triangles Congruent ASA and AAS • The ASA postulate can be used to prove a related triangle congruence theorem Theorem 5.1 Angle-Angle-Side Congruence Theorem (AAS) • If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. Paragraph Proof of AAS Theorem Given triangles ABC and XYZ with corresponding congruent angles and non-included side as shown. Angles C and Z are also congruent by the triangle sum theorem. Therefore the two triangles are congruent by the ASA postulate.

  3. Proving Triangles Congruent ASA and AAS Two-column Proof of AAS Theorem Given triangles ABC and XYZ as marked • Finally, AAA is not a congruence shortcut because it is possible to construct an infinite number of triangles with the same three angle measures

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