1 / 3

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?

charity
Download Presentation

Proving Triangles Congruent ASA and AAS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related