1. 4.3: Analyzing Triangle Congruence
Expectations:
G2.3.1: Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria and that right triangles are congruent using the hypotenuse-leg criterion.
G2.3.2:Use theorems about congruent triangles to prove additional theorems and solve problems, with and without use of coordinates.
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4.3: Analyzing Triangle Congruence

2. 4.3: Analyzing Triangle Congruence
AAA Conjecture
a. Draw a 30°, 60°, 90 right triangle.
b. Compare your triangle to a neighbor’s.
c. What can be said about the triangles?
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4.3: Analyzing Triangle Congruence

3. 4.3: Analyzing Triangle Congruence
AAA Conjecture
AAA is not sufficient to conclude triangles are congruent.
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4.3: Analyzing Triangle Congruence

4. 4.3: Analyzing Triangle Congruence
SSA Conjecture
a. Draw a triangle with 2 sides that are 8cm and 6 cm, with a non-included angle of 40.
b. Compare your triangle to a neighbor’s.
c. What can be said about the triangles?
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4.3: Analyzing Triangle Congruence

5. 4.3: Analyzing Triangle Congruence
SSA Conjecture
SSA is not sufficient to prove triangles are congruent.
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4.3: Analyzing Triangle Congruence

6. 4.3: Analyzing Triangle Congruence
SsA
A very special case of SSA is valid for proving triangles congruent. It is referred to as SsA. In SsA, the angles given must be opposite the longer of the 2 sides.
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4.3: Analyzing Triangle Congruence

7. 4.3: Analyzing Triangle Congruence
SsA E B F C D A
Given the above information, ΔABC  ΔDEF.
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4.3: Analyzing Triangle Congruence

8. 4.3: Analyzing Triangle Congruence
SsA
In two triangles, if two sides of the first are congruent to two sides of the second and the angle opposite the longer of the two sides of the first is congruent to the corresponding angle of the second triangle, then the triangles are congruent.
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4.3: Analyzing Triangle Congruence

9. Are the triangles congruent? Justify your answer.Z C
10 in
10 in
50º
60º
50º
60º A B Y X
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4.3: Analyzing Triangle Congruence

10. 4.3: Analyzing Triangle Congruence
Non-Included Sides C
AC is a
nonincluded
side for A
and B
BC is a
nonincluded
side for A
and B B A
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4.3: Analyzing Triangle Congruence

11. AAS Congruence Theorem
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of the second triangle, then the triangles are congruent.
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4.3: Analyzing Triangle Congruence

12. 4.3: Analyzing Triangle Congruence
HL Congruence Theorem
In 2 right triangles, if the hypotenuse and a leg of the first are congruent to the hypotenuse and a leg of the second, then the triangles are congruent.
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4.3: Analyzing Triangle Congruence

13. Prove the HL Congruence TheoremF C A B D E
Given: AC = DF and BC = EF
Prove: ABCDEF
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4.3: Analyzing Triangle Congruence

14. 4.3: Analyzing Triangle Congruence
Assignment
pages ,
# (evens), (all), 30, 32, 34, 35, 37, 42, 43
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4.3: Analyzing Triangle Congruence