Proving Congruence – SSS, SAS

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Transcript 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