Download Honors Math 2 Name: Triangle Congruence Postulates (Section 6.0

Honors Math 2
Triangle Congruence Postulates (Section 6.0)
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Congruent figures have the same size and shape. This means that all pairs of corresponding
parts have equal measures. We say this means the corresponding parts are congruent.
Congruent triangles have six pairs of corresponding parts that are congruent: three pairs of
congruent angles and three pairs of congruent sides.
We do not need to prove all six corresponding parts are congruent. There are several shortcuts:
•
SSS
o If three sides of one triangle are congruent to the corresponding sides of the other
triangle, then the two triangles are congruent.
•
SAS
o If two sides and the included angle of one triangle are congruent to the
corresponding parts of the other triangle, then the two triangles are congruent.
•
ASA
o If two angles and the included side of one triangle are congruent to the
corresponding parts of the other triangle, then the two triangles are congruent.
•
AAS
o If two angles and a non-included side of one triangle are congruent to the
corresponding parts of the other triangle, then the two triangles are congruent.
Why is ΔRXV ≅ ΔHTL ? If no method works, write ‘not possible’.
• To begin, draw a picture and label all the known information.
• Decide by what method the triangles are congruent.
Given Information
1.
2.
3.
4.
5.
Picture
Answer
(SSS, SAS, ASA,
AAS)
RV ≅ HL, VX ≅ LT ,
∠V ≅ ∠L
∠X ≅ ∠T , ∠R ≅ ∠H ,
XV ≅ TL
RX ≅ HT , RV ≅ HL,
∠X ≅ ∠T
∠V ≅ ∠L, ∠R ≅ ∠H ,
VR ≅ LH
RX ≅ TL, ∠R ≅ ∠H ,
∠X ≅ ∠T
Figure out what else you would need to prove ΔKMN ≅ ΔPQR by the given method.
• To begin, draw a picture and label all the known information.
• Decide if you need an additional side or an additional angle
• Decide what else you need to know to prove the triangles congruent using the given method.
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•
Proof
Answer
Given Information
Picture
Method
(what else do you need?)
6.
∠K = ∠P, ∠N = ∠R
AAS
7.
KM ⊥ MN
PQ ⊥ QR, KM = PQ
SAS
KM = PQ
ASA
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