prove triangles congruent by asa & aas lesson 4.10 (m1) use two more methods to prove triangle...
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Prove Triangles Congruent by ASA &
AAS
Lesson 4.10 (M1)Use two more methods to prove triangle congruence
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Vocabulary A flow proof uses arrows to show the flow of
a logical argument. ASA Congruence Postulate: If two angles
and the included side of one triangle are congruent to two angles of a second triangle, then the two triangles are congruent
AAS Congruence Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
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ASA Congruence Postulate
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AAS Congruence Theorem
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GUIDED PRACTICE for Examples 1 and 2
SOLUTION
1.
GivenS U
The vertical angles are congruent
RTS UTV
GivenRS UV
STATEMENTS REASONS
In the diagram at the right, what postulate or theorem can you use to prove that RST VUT ? Explain.
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GUIDED PRACTICE for Examples 1 and 2
Therefore are congruent because vertical angles are congruent so two pairs of angles and a pair of non included side are congruent. The triangle are congruent by AAS Congruence Theorem.
RTS UTV
ANSWER
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GUIDED PRACTICE for Examples 1 and 2
2.
1. Draw BD parallel to AC . 1. Parallel Postulate
PROVE 3 = 180°1m 2m m+ +
2. Angle Addition Postulate and definition of straight angle
2. 4m 2m 5m+ + = 180°
3. Alternate Interior Angles Theorem
3. 1 4 , 3 5
5. Substitution Property of Equality
5. 1m 2m 3m+ + = 180°
4. Definition of congruent angles
4. 1m = 4m 3m = 5m,
STATEMENTS REASONS
GIVEN ABC
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