Transcript Geo 4.3 4.3 Triangle Congruence AAS and ASA

Warm Up
1. What are sides AC and BC called? Side
AB?
legs; hypotenuse
2. Which side is in between A and C?
AC
3. Given DEF and GHI, if D  G and
E  H, why is F  I?
Third s Thm.
An included side is the common side
of two consecutive angles in a polygon.
The following postulate uses the idea of
an included side.
4-3 Triangle Congruence by ASA
and AAS
Learning Target:
I can Prove triangles congruent by
using ASA and AAS.
Example 2: Applying ASA Congruence
Determine if you can use ASA to prove the
triangles congruent. Explain.
Two congruent angle pairs are give, but the included
sides are not given as congruent. Therefore ASA
cannot be used to prove the triangles congruent.
Check It Out! Example 2
Determine if you can use ASA to
prove NKL  LMN. Explain.
By the Alternate Interior Angles Theorem. KLN  MNL.
NL  LN by the Reflexive Property. No other congruence
relationships can be determined, so ASA cannot be
applied.
You can use the Third Angles Theorem to prove
another congruence relationship based on ASA. This
theorem is Angle-Angle-Side (AAS).
Table Assignments
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Table 1 – P. 232 #29
Table 2 – P. 239 #14
Table 3 – P. 238 #12
Table 4 - P. 232 #28
Table 5 – P. 239 #20
Table 6 – P. 240 #26
Table 7 – P. 232 #30
Table 8 – P. 232 #31
Homework Assignment
Foundation – p. 238 8-18
Core – 19-26
Challenge - 29
Check It Out! Example 3
Use AAS to prove the triangles congruent.
Given: JL bisects KLM, K  M
Prove: JKL  JML
Lesson Quiz: Part II
4. Given: FAB  GED, ABC   DCE, AC  EC
Prove: ABC  EDC
Lesson Quiz: Part I
Identify the postulate or theorem that proves
the triangles congruent.
ASA
SAS or SSS
Statements
Reasons
Lesson Quiz: Part II Continued
FAB  GED
1. Given
AC is a supp. of;
is a supp. of GED.
2. Def. of supp. s
BAC  DC
3.  Supp. Thm.
E
ACB  DCE; AC  EC
4. Given
ABC  EDC
5. ASA Steps 3,4
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