Triangle congruence ASA and AAS

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Triangle congruence ASA and AAS
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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

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Use ASA to find the missing sides

• AB 18, BC 17, AC 6

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CAUTION

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

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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

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Find the area of each triangle using AAS
congruence

• PQ 6, QR 4x-2, UT 3x 1

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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.

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See Example 5 p. 190
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4 ways to prove triangle congruence

• 1. SSS postulate
• 2. SAS postulate
• 3. ASA postulate
• 4. AAS postulate

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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

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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

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

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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

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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

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