1 / 15

Proving Triangle Congruence: ASA and AAS Postulates

Learn how to prove triangle congruence with examples using ASA and AAS postulates. Understand when triangles are congruent and explore concepts like bisectors, perpendicular lines, and vertical angles. Practice with flow proofs and complete homework assignments.

morgandebra
Download Presentation

Proving Triangle Congruence: ASA and AAS Postulates

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. Do Now

  2. Geometry 4.6: Prove Triangles Congruent by ASA and AAS

  3. Postulate 21: Angle-Side-Angle (ASA) • If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. • Example: because of ASA. P L Q R M N

  4. Theorem 4.6: Angle-Angle-Side (AAS) • If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of a second triangle, then the two triangles are congruent. • Example: because of AAS. P L Q R M N

  5. Triangles are congruent when you have… SSS AAS SAS ASA HL

  6. Triangles are not congruent when you have… ASS AAA

  7. Review from old chapters • Bisector: Cuts the segment or angle into two congruent pieces. • Midpoint of a segment: Cuts the segment into two congruent pieces. • Perpendicular lines: Two lines that intersect at a right angle (90 degrees). • Vertical angles: Angles “across” from each other- they are congruent to each other.

  8. Are the triangles congruent, if yes write a congruence statement and explain using SSS, SAS, ASA, AAS, HL . 1.) B D C is the midpoint of AE A C E

  9. Are the triangles congruent, if yes write a congruence statement and explain using SSS, SAS, ASA, AAS, HL . 2.) P Q R S

  10. Are the triangles congruent, if yes write a congruence statement and explain using SSS, SAS, ASA, AAS, HL . 3.) I K T E

  11. Examples

  12. Complete the Proof

  13. Flow Proof • Uses arrows to show the flow of a logical argument. • Each reason is written below the statement it justifies.

  14. Write a Flow Proof

  15. Homework • Textbook page 250-251 • #4-20 evens

More Related