1 / 21

Understanding Congruence in Triangles: Proof and Properties

This guide covers the concept of triangle congruence, detailing the conditions two triangles must meet to be considered congruent, including corresponding sides and angles. It explains the significance of congruent triangles, highlighting the roles of midpoints and vertical angles. The properties of congruent triangles, including reflexive, symmetric, and transitive properties, are also discussed. Students will learn to identify congruent triangles, demonstrate proofs, and solve related problems.

knoton
Télécharger la présentation

Understanding Congruence in Triangles: Proof and Properties

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. 4.2 Congruence and Triangles Prove two triangles congruence

  2. Congruent triangles Congruent triangles have congruent angles and sides. The angles and sides must correspond. Congruent corresponding sides and corresponding angles. Meaning AB = XY; BC = YZ; AC = XZ and

  3. Name the congruent triangles Make sure the letters are in the appropriate order.

  4. Figures can be congruent If the sides and angles of two figures correspond, then the two figures are congruent. NOLM ≈ YXWZ

  5. Figures can be congruent If the sides and angles of two figures correspond, then the two figures are congruent. NOLM ≈ YXWZ

  6. Solve for k

  7. Which Triangles are congruent and why?

  8. Which Triangles are congruent and why? All the sides and angles are congruent

  9. Given: , O is the midpoint of MQ and PN Prove:

  10. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN

  11. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; PO = NO

  12. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; #2. Def. of midpoint PO = NO

  13. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; #2. Def. of midpoint PO = NO #3.

  14. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; #2. Def. of midpoint PO = NO #3. #3. Vert. angles ≈

  15. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; #2. Def. of midpoint PO = NO #3. #3. Vert. angles ≈ #4.

  16. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; #2. Def. of midpoint PO = NO #3. #3. Vert. angles ≈ #4. #4. Alt. Int. Angles ≈

  17. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; #2. Def. of midpoint PO = NO #3. #3. Vert. angles ≈ #4. #4. Alt. Int. Angles ≈ #5.

  18. Given: , O is the midpoint of MQ and PN Prove: #1. O is the midpt. of #1. Given MQ and PN #2. MO = OQ; #2. Def. of midpoint PO = NO #3. #3. Vert. angles ≈ #4. #4. Alt. Int. Angles ≈ #5. #5. All parts are congruent

  19. Properties of congruent Triangles Reflexive Symmetric Transitive ( not substitution ) As any twin can tell you, even if they look alike does not make them the same person.

  20. Homework Page 206 – 210 # 10 – 28 even, 39, 42 – 56 even

  21. Homework Page 206 – 210 # 11 – 29 odd, 30 – 35, 57

More Related