#### Proving Congruence – SSS, SAS

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Proving Congruence – SSS, SAS

Proving Congruence – SSS, SAS
Side-Side-Side Congruence
Postulate (SSS)
• If the sides of one triangle are
congruent to the sides of a second
triangle, then the triangles are
congruent.
Write a two-column proof to prove that ABC
Proof:
Statements
Reasons
1.
2.
3. ABC
1. Given
2. Reflexive
3. SSS
GBC
GBC if
Determine whether ABC DEF for A(5, 5), B(0, 3),
C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain.
Answer:
By definition
of congruent segments, all corresponding
segments are congruent. Therefore,
ABC DEF by SSS.
Proving Congruence – SSS, SAS
Included angle – In a triangle, an angle that is
formed by two sides is between them and, thus,
referred to as included by those two sides.
Side-Angle-Side Congruence Postulate
(SAS)
• If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent.
Write a flow proof.
Given:
Prove: ABC ADC
.
Proof:
Determine which postulate can be used to prove that
the triangles are congruent. If it is not possible to
prove that they are congruent, write not possible.
a.
Answer: SAS
b.
Answer: not possible