holt geometry 4-5 triangle congruence: asa and aas 4-5 triangle congruence: asa and aas holt...
TRANSCRIPT
Holt Geometry
4-5 Triangle Congruence: ASA and AAS4-5 Triangle Congruence: ASA and AAS
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Do Now
1. What are sides AC and BC called? Side AB?
2. Which side is in between A and C?
3. Given DEF and GHI, if D G and E H, why is F I?
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
• Apply ASA and AAS to construct triangles and to solve problems.
• Prove triangles congruent by using ASA and AAS.
Objectives
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
included side
Vocabulary
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Example 1: Applying ASA Congruence
Determine if you can use ASA to prove the triangles congruent. Explain.
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Example 2
Determine if you can use ASA to prove NKL LMN. Explain.
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Example 3: Using AAS to Prove Triangles Congruent
Use AAS to prove the triangles congruent.
Given: X V, YZW YWZ, XY VY
Prove: XYZ VYW
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Lesson Quiz: Part I
Identify the postulate or theorem that proves the triangles congruent, or determine “not possible.”
ASA
not possible
SAS or SSS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
Congruence Postulates Extra Examples
SSS, ASA, SAS, AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
1. Given: ÐA @ÐDAB @ DEÐB @ ÐE.
ASA
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
2. Given: ÐC @ÐFÐB @ ÐE
AC @ DF.
AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
3. Given: ÐC @ÐF
ÐB @ ÐE
BC @ EF.
ASA
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
4. Given: ÐC @ÐF
AC @ DF
BC @ EF.
SAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
5. Given: ÐA @ÐD
ÐC @ ÐF
BC @ EF.
AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
6. Given: AB @ DE
BC @ EF
AC @ DF.
SSS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
7. Given: ÐC and ÐF are rt. Ðs AB @ DE
ÐA @ ÐD.
AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
8. Given: ÐC and ÐF are rt. Ðs AC @ DF
ÐB @ ÐE.
AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
9. Given: ÐC @ÐF
ÐB @ ÐE
AC @ DF.
AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
10. Given: ÐC and ÐF are rt. Ðs
ÐB @ ÐE
BC @ EF.
ASA
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
11. Given: ÐA @ÐD
AB @ DE
ÐB @ ÐE.
ASA
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
12. Given: ÐA @ÐD
ÐC @ ÐF
BC @ EF.
AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
13. Given: BC ^ AC
EF ^ DF
AB @ DE
ÐB @ ÐE.
AAS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
14. Given: AB @ DE
BC @ EF
AC @ DF.SSS
Holt Geometry
4-5 Triangle Congruence: ASA and AAS
15. Given: ÐC @ÐF
AC @ DF
BC @ EF.SAS