Title: Triangle congruence ASA and AAS
1Triangle congruence ASA and AAS
2Angle-side-angle (ASA) congruence
postulatePostulate 16
- If 2 angles and the included side of 1 triangle
are congruent to 2 angles and the included side
of another triangle , then the triangles are
congruent
3Use ASA to find the missing sides
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4CAUTION
- Be sure the congruent side is an included side of
the 2 congruent angles when using ASA
5Angle-angle-side (AAS) triangle congruence
theoremtheorem 30-1
- If 2 angles and a nonincluded side of 1 triangle
are congruent to 2 angles and the nonincluded
side of another triangle, then the triangles are
congruent
6Find the area of each triangle using AAS
congruence
7Using AAS in a proof
- GivenOM bisects ltNML, ltNltL
- Prove triangle NOM is congruent to triangle LOM
- Statements Reasons
- 1. ltN is congruent to ltL 1.
- 2. ltNMO is cong ltLMO 2.
- 3.MOMO 3.
- 4. tri NOM tri LOM 4.
8See Example 5 p. 190
94 ways to prove triangle congruence
- 1. SSS postulate
- 2. SAS postulate
- 3. ASA postulate
- 4. AAS postulate
10Right triangle congruence theorems
- It is assumed in all right angle congruence
theorems that the measure of the right angle is
already known, so it only takes 2 other congruent
parts to prove congruency
11Leg-angle (LA) right triangle congruence theorem-
theorem 36-1
- If a leg and an acute angle of 1 right triangle
are congruent to a leg and an acute angle of
another right triangle, then the triangles are
congruent
12The Leg-Angle Right Triangle Congruence Theorem
follows from the ASA postulate and the AAS theorem
13Hypotenuse-Angle (HA) Right Triangle Congruence
Theoremtheorem 36-2
- If a hypotenuse and an acute angle of 1 right
triangle are congruent to the hypotenuse and an
acute angle of another right triangle, then the
triangles are congruent
14Leg-Leg (LL) Right Triangle Congruence
TheoremTheorem 36-3
- If 2 legs of 1 right triangle are congruent to 2
legs of another right triangle , then the
triangles are congruent
15Hypotenuse-Leg (HL) Right Triangle Congruence
Theoremtheorem 36-4
- If the hypotenuse and a leg of 1 right triangle
are congruent to the hypotenuse and a leg of
another right triangle, then the triangles are
congruent
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