Ways to prove Triangles Congruent (SSS), (SAS), (ASA)

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Ways to prove Triangles Congruent (SSS), (SAS),
(ASA)

• 4-2 to 4-4

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EXAMPLE 4
Use the Third Angles Theorem
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EXAMPLE 5
Prove that triangles are congruent
Plan for Proof
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EXAMPLE 5
Prove that triangles are congruent
Plan in Action
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for Examples 4 and 5
GUIDED PRACTICE
SOLUTION
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for Examples 4 and 5
GUIDED PRACTICE
SOLUTION
(Proved from above sum)
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for Examples 4 and 5
GUIDED PRACTICE
Given
Given
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EXAMPLE 1
Identify congruent parts
SOLUTION
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EXAMPLE 2
Use properties of congruent figures
SOLUTION
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EXAMPLE 2
Use properties of congruent figures
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EXAMPLE 3
Show that figures are congruent
SOLUTION
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EXAMPLE 3
Show that figures are congruent
Then, 1 4 and 2 3 by the
Alternate Interior Angles Theorem. So, all pairs
of corresponding angles are congruent.
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for Examples 1, 2, and 3
GUIDED PRACTICE
SOLUTION
Corresponding sides
Corresponding angles
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for Examples 1, 2, and 3
GUIDED PRACTICE
SOLUTION
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for Examples 1, 2, and 3
GUIDED PRACTICE
SOLUTION
In the given diagram
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EXAMPLE 1
Use the SSS Congruence Postulate
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for Example 1
GUIDED PRACTICE
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
Three sides of one triangle are congruent to
three sides of second triangle then the two
triangle are congruent.
Yes. The statement is true.
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for Example 1
GUIDED PRACTICE
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
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for Example 1
GUIDED PRACTICE
Therefore the given statement is false and
ABC is not Congruent to CAD because
corresponding sides are not congruent
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for Example 1
GUIDED PRACTICE
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
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EXAMPLE 1
Use the SAS Congruence Postulate
Write a proof.
GIVEN
PROVE
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EXAMPLE 1
Use the SAS Congruence Postulate
STATEMENTS
REASONS

ABC CDA
SAS Congruence Postulate
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EXAMPLE 2
Use SAS and properties of shapes
In the diagram, QS and RP pass through the center
M of the circle. What can you conclude about
MRS and MPQ?
SOLUTION
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for Examples 1 and 2
GUIDED PRACTICE
In the diagram, ABCD is a square with four
congruent sides and four right angles. R, S, T,
and U are the midpoints of the sides of ABCD.
Also, RT SU and .
SU VU
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for Examples 1 and 2
GUIDED PRACTICE

BSR DUT
Prove that
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EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
Write a proof.
SOLUTION
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EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
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EXAMPLE 4
Choose a postulate or theorem
Sign Making
You are making a canvas sign to hang on the
triangular wall over the door to the barn shown
in the picture. You think you can use two
identical triangular sheets of canvas. You know
that RP QS and PQ PS . What postulate or
theorem can you use to conclude that PQR
PSR?
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EXAMPLE 4
Choose a postulate or theorem
SOLUTION
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for Examples 3 and 4
GUIDED PRACTICE
Use the diagram at the right.
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for Examples 3 and 4
GUIDED PRACTICE
Use the diagram at the right.

Use the information in the diagram to prove that
ACB DBC
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for Examples 3 and 4
GUIDED PRACTICE
STATEMENTS
REASONS