Triangle Congruency

MM1G3 c

Congruency Postulates/Theorems

SSS Congruency Postulate

Side-Side-Side (SSS) Congruence Examples

The Side-Side-Side (SSS) Congruence Postulate states that if all three sides of one triangle are congruent to all three sides of another triangle, then the two triangles are congruent.

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Example 1: In the triangles below, MN = 3, NP = 4, MP = 5, XY = 3, YZ = 4, and XZ = 5. Are the two triangles congruent? If so, why?

Solution:

ZY

X

PN

M

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(SSS) Side-Side-Side by the Therefore,

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XYZMNP

XZMPYZNPXZMP

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XYMNXYMN

Example 2: If x = 4, are the two triangles below congruent? If so, why?

Solution: Substituting x = 4, we can find the length of each side.

QP = 10, QR = 12, and PR = 9

KL = 10, KJ = 12, and LJ = 9

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K

RP

Q

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2x+1

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3x-3

Example 3: Is ∆ ABD congruent to ∆ CDB? If so, why?

Solution:

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LJ

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Therefore, since all three sides of ∆ QPR are congruent to all three sides of ∆ KLJ, then the two triangles are congruent by the Side-Side-Side (SSS) Congruence Postulate.

Summary

Side-Side-Side (SSS) Congruence Postulate:

If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

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