Download Triangle Congruence Theorems

The Side-Side-Side
Congruence Postulate (SSS)
Triangle Congruence
Theorems
• If the three sides of one triangle are
congruent to the three sides of another
triangle, then the triangles are congruent
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Mathematics 12 Advanced
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The Side-Angle-Side
Congruence Postulate (SAS)
The Angle-Side-Angle
Congruence Postulate (ASA)
• If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of a second triangle, then
the triangles are congruent
• If two angles and the included side of one
triangle are congruent to two angles and
the included side of a second triangle,
then the triangles are congruent
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The Side-Angle-Angle
Congruence Postulate (SAA)
• If two angles and a non-included side of
one triangle are congruent to two angles
and a non-included side of a second
triangle, then the triangles are congruent
The Hypotenuse-Leg
Congruence Postulate (HL)
• If the hypotenuse and a leg of one right
triangle are congruent to the hypotenuse
and a leg of a second right triangle, then
the triangles are congruent
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TP
is the perpendicular bisector of
V
Proof using triangle
congruence theorems
Example 1
Given:
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AC
Prove: ∆TAC is isosceles
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Statements
Reasons
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Example 2
Given: The figure as marked
Prove: AB = ED
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Example 3
Proof using
triangle
congruence
theorems
Statements
Given: PQ // ST
PQ = ST
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QT = RU
Prove:
PR = SU
Reasons
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