Unit 2 Part 4 Proving Triangles Congruent. Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles.
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Unit 2 Part 4
Proving Triangles Congruent
Angle – Side – Angle Postulate If two angles and the included side
of a triangle are congruent to two angles and the included side of another triangle, then they are congruent by ASA.
Included means between
Example of ASA
A
F
E
D
C
B
The side is between the angles.
Angle - Angle - Side Postulate If two consecutive angles and a
side of a triangle are congruent to two consecutive angles and a side of another triangle, then the triangles are congruent by AAS.
Consecutive means one after another.
Note: the side is NOT between the angles
Example of AAS
F
E
D
C
B
A
The side is not between the angles.
Recall Reflexive Property : such as segment
AB is congruent segment AB Vertical Angles are congruent such as
angle G is congruent to angle HB
ADC
G H
A
S
A
A
A
S
Hypotenuse-Leg Theorem
(HL Theorem) If the hypotenuse and leg of a
right triangle is congruent to the hypotenuse and leg of another right triangle then they are congruent.
R
H
L
CPCTC
Corresponding Parts of Congruent Triangles are Congruent.
Once you prove two triangles congruent, then all of their corresponding parts are congruent.
SSS Side – Side – Side SAS Side – Angle – Side AAS Angle – Angle – Side ASA Angle – Side – Angle HLT Hypotenuse – Leg – Theorem Reflexive Property Vertical Angles CPCTC (corresponding parts of
congruent triangles are congruent)
What you should remember
S
S
A
Statement Reason
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