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Triangle congruence ASA and AAS

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Use ASA to find the missing sides. AB =18, BC = 17, AC = 6. 18. CAUTION ... Find the area of each triangle using AAS congruence. PQ = 6, QR = 4x-2, UT = 3x 1 ... – PowerPoint PPT presentation

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Title: Triangle congruence ASA and AAS


1
Triangle congruence ASA and AAS
2
Angle-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

3
Use ASA to find the missing sides
  • AB 18, BC 17, AC 6

18
4
CAUTION
  • Be sure the congruent side is an included side of
    the 2 congruent angles when using ASA

5
Angle-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

6
Find the area of each triangle using AAS
congruence
  • PQ 6, QR 4x-2, UT 3x 1

7
Using 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.

8
See Example 5 p. 190
9
4 ways to prove triangle congruence
  • 1. SSS postulate
  • 2. SAS postulate
  • 3. ASA postulate
  • 4. AAS postulate

10
Right 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

11
Leg-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

12
The Leg-Angle Right Triangle Congruence Theorem
follows from the ASA postulate and the AAS theorem
13
Hypotenuse-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

14
Leg-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

15
Hypotenuse-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

16
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