1 / 15

4.4 Proving Triangles are Congruent: ASA and AAS

4.4 Proving Triangles are Congruent: ASA and AAS. Objectives/Assignment. Prove that triangles are congruent using the ASA Congruence Postulate and the AAS Congruence Theorem Use congruence postulates and theorems in real-life problems Assignment: 2-22 even, 32-37 all, quiz page 227.

Download Presentation

4.4 Proving Triangles are 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. 4.4 Proving Triangles are Congruent: ASA and AAS

  2. Objectives/Assignment • Prove that triangles are congruent using the ASA Congruence Postulate and the AAS Congruence Theorem • Use congruence postulates and theorems in real-life problems • Assignment: 2-22 even, 32-37 all, quiz page 227

  3. 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 triangles are congruent. Goal 1: Using the ASA and AAS Congruence Methods Postulate 21: Angle-Side-Angle (ASA) Congruence Postulate

  4. 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 triangles are congruent. Theorem 4.5: Angle-Angle-Side (AAS) Congruence Theorem

  5. Given: A  F, C  D, BA  EF Prove: ∆ABC  ∆DEF Theorem 4.5: Angle-Angle-Side (AAS) Congruence Theorem

  6. You are given that two angles of ∆ABC are congruent to two angles of ∆DEF. By the Third Angles Theorem, the third angles are also congruent. That is, B  E. Notice that BC is the side included between B and C, and EF is the side included between E and F. You can apply the AAS Congruence Postulate to conclude that ∆ABC  ∆DEF. Theorem 4.5: Angle-Angle-Side (AAS) Congruence Theorem

  7. Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. Example 1: Developing Proof

  8. In addition to the angles and segments that are marked, EGF JGH by the Vertical Angles Theorem. Two pairs of corresponding angles and one pair of corresponding sides are congruent. You can use the AAS Congruence Theorem to prove that ∆EFG  ∆JHG. Example 1: Developing Proof

  9. Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. Example 1: Developing Proof

  10. In addition to the congruent segments that are marked, NP  NP. Two pairs of corresponding sides are congruent. This is not enough information to prove the triangles are congruent. Example 1: Developing Proof

  11. Is it possible to prove the triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning. UZ║WX AND UW ║ ZX Example 1: Developing Proof 1 2 3 4

  12. The two pairs of parallel sides can be used to show 1  3 and 2  4. Because the included side WZ is congruent to itself, ∆WUZ  ∆ZXW by the ASA Congruence Postulate. Example 1: Developing Proof 1 2 3 4

  13. Given: AD ║CE, BD  BC Prove: ∆ABD  ∆EBC Plan for proof: Notice that ABD and EBC are congruent. You are given that BD  BC . Use the fact that AD ║EC to identify a pair of congruent angles. Example 2: Proving Triangles are Congruent

  14. Statements: BD  BC AD ║ EC D  C ABD  EBC ∆ABD  ∆EBC Reasons: Given Given Alternate Interior Angles Vertical Angles Theorem ASA Congruence Theorem Proof

  15. Note • You can often use more than one method to prove a statement.

More Related