This document discusses congruent triangles. It defines congruent as having the same measure or size and shape. There are three congruence postulates discussed: SSS, SAS, and ASA. SSS states that two triangles are congruent if all three sides of one triangle are equal to all three sides of the other triangle. SAS states that two triangles are congruent if two sides and the included angle of one triangle are equal to those of the other triangle. ASA states that two triangles are congruent if two angles and the included side of one triangle are equal to those of the other triangle. Examples are provided to demonstrate applying the postulates.

1. Ch4.2_CongruentTriangles.notebook October 24, 2011
Chapter 4.2
Congruent Triangles
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2. Ch4.2_CongruentTriangles.notebook October 24, 2011
Congruent means same measure (or size and shape)
≅
Congruent triangles have
congruent angles and
congruent sides B
X
Y Z
A C
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3. Ch4.2_CongruentTriangles.notebook October 24, 2011
Types of Triangle Congruences
The SSS Postulate
(side­side­side)
2 triangles are congruent if:
3 sides of one triangle are equal to
the 3 sides of the other triangle
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4. Ch4.2_CongruentTriangles.notebook October 24, 2011
Types of Triangle Congruences
The SAS Postulate
(side­angle­side)
2 triangles are congruent if:
2 sides and their included angle of one
triangle are equal to 2 sides and their
included angle of the other triangle
Included angle
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5. Ch4.2_CongruentTriangles.notebook October 24, 2011
Types of Triangle Congruences
The ASA Postulate
(angle­side­angle)
2 triangles are congruent if:
2 angles and their included side of one
triangle are equal to 2 angles and their
included side of the other triangle
Included side
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6. Ch4.2_CongruentTriangles.notebook October 24, 2011
Are the following triangles congruent?
If so, by what congruence postulate?
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7. Ch4.2_CongruentTriangles.notebook October 24, 2011
Which Postulate?
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8. Ch4.2_CongruentTriangles.notebook October 24, 2011
Prove: ΔVWX ≅ ΔZXY
Statement Reason
Definition of
perpendicular
lines
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9. Ch4.2_CongruentTriangles.notebook October 24, 2011
Given: RQ = RS R
RT bisects <QRS
Prove: ΔQRT = ΔSRT
T
Q S
Statement Reason
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10. Ch4.2_CongruentTriangles.notebook October 24, 2011
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