Proving Triangles are Congruent: SSS and SAS

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Proving Triangles are CongruentSSS and SAS

• Chapter 4.3

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Objectives/Assignment

• Prove that triangles are congruent using the SSS
  and SAS congruence postulate
• Use congruence postulates in real life problems
• Assignment 2-28 even, 44-46 all

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Postulate 19 (SSS) Side-Side-Side Congruence
Postulate
Goal 1 SSS SAS Congruence Postulates

• If three sides of one triangle are congruent to
  three sides of a second triangle, then the two
  triangles are congruent.

Side BC EF, and
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Proof
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Postulate 20 (SAS) Side-Angle-Side Congruence
Postulate

• If two sides and the included angle of one
  triangle are congruent to two sides and the
  included of a second triangle, then the two
  triangles are congruent.

If Side QS YZ, Side PS XZ,
PQS
XYZ
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Proof
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Example 3 Choosing Which Congruence Postulate to
Use
Goal 2 Modeling a Real Life Situation
Paragraph Proof
The marks on the diagram show that PQ ? PS and
QR ? SR. By the Reflexive Property of
Congruence, RP ? RP. Because the sides of ?PQR
are congruent to the corresponding sides of ?PSR,
you can use the SSS Congruence Postulate to prove
that the triangle are congruent.
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Example 6 Congruent Triangles in a Coordinate
Plane

• Use the SSS Congruence Postulate to show that
  ABC FGH.

AC FH 3 AB FG 5 AB FG
Use the Distance Formula to find the lengths BC
and GH
H(6,5)
A(-7,5)
C(-4,5)
Who remembers the distance formula?
F(6,2)
G(1,2)
B(-7,0)
BC GH v34 All sides congruent