1 / 11

4.3 - Triangle Congruence by ASA and AAS

4.3 - Triangle Congruence by ASA and AAS. Postulate 4-3 Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.  UVT   XYW.

cheri
Download Presentation

4.3 - Triangle Congruence by 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. 4.3 - Triangle Congruence by ASA and AAS

  2. Postulate 4-3 Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. UVT  XYW

  3. Theorem 4-2 Angle-Angle-Side (AAS) Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent. APX  BPY

  4. Which theorem or postulate, if any, could you use to prove that the two triangles are congruent? If possible, write the congruence statement. Not enough information. ASA ∆TVS ∆VTU

  5. Which theorem or postulate, if any, could you use to prove that the two triangles are congruent? If possible, write the congruence statement. AAS ∆WYX ∆AYZ AAS ∆EBC ∆FDC

  6. Which theorem or postulate, if any, could you use to prove that the two triangles are congruent? If possible, write the congruence statement. AAS ∆DEH ∆GEF Not enough information

  7. Given:A  R , RA  DE Prove: RDE  ADE Statements Reasons • _______ • __________ • __________ • __________ • __________ • __________ are rt. angles RDE  ADE Use to complete proof: Given, Definition of Perpendicular Lines, Reflexive Property of Congruence, All Right Angles are Congruent, SSS, SAS, ASA, AAS.

  8. Given:A  R , RA  DE Prove: RDE  ADE Statements Reasons • Given • Given • Definition of Perpendicular Lines • All right angles are congruent • Reflexive Property of Congruence • AAS are rt. angles RDE  ADE

  9. Given: CE bisects AD, AE || CD Prove: ABE  DBC Statements Reasons 1. ___________ 2. ___________ 3. ___________ 4. ___________ 5. ___________ 6. ___________ CE bisects AD AE || CD ABE  DBC Use to complete proof: Alternate Interior Angles are Congruent, Given, Definition of Segment Bisector, SSS, SAS, AAS, ASA.

  10. Given: CE bisects AD, AE || CD Prove: ABE  DBC Statements Reasons Given Definition of segment bisector Given Alternate Interior Angles are Congruent Alternate Interior Angles are Congruent AAS CE bisects AD AE || CD ABE  DBC

  11. Summary: To prove two triangles are congruent, use SSS, SAS, ASA or AAS. (one more later - there are five ways altogether)

More Related