Transcript Triangle congruence ASA and AAS

Triangle
congruence
ASA and AAS
Angle-side-angle (ASA)
congruence postulate
Postulate 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
Use ASA to find the missing
sides
• AB =18, BC = 17, AC = 6
18
CAUTION
• Be sure the congruent
side is an included
side of the 2 congruent
angles when using
ASA
Angle-angle-side (AAS)
triangle congruence theorem
theorem 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
Find the area of each triangle
using AAS congruence
• PQ = 6, QR = 4x-2, UT = 3x +1
Using AAS in a proof
• Given:OM bisects <NML, <N=<L
• Prove: triangle NOM is congruent to triangle
LOM
• Statements
Reasons
• 1. <N is congruent to <L 1.
• 2. <NMO is cong <LMO 2.
• 3.MO=MO
3.
• 4. tri NOM = tri LOM
4.
See Example 5
p. 190
4 ways to prove triangle
congruence
• 1. SSS postulate
• 2. SAS postulate
• 3. ASA postulate
• 4. AAS postulate
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
Leg-angle (LA) right triangle
congruence theoremtheorem 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
The Leg-Angle Right
Triangle Congruence
Theorem follows from
the ASA postulate and
the AAS theorem
Hypotenuse-Angle (HA) Right
Triangle Congruence Theorem
theorem 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
Leg-Leg (LL) Right Triangle
Congruence Theorem
Theorem 36-3
• If 2 legs of 1 right triangle are congruent to
2 legs of another right triangle , then the
triangles are congruent
Hypotenuse-Leg (HL) Right
Triangle Congruence Theorem
theorem 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