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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
4. Proving Triangles Congruent-ASA, AAS
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Exercise 10 Page 368

Identify the pair of vertical angles. Use the Alternate Interior Angles Theorem to determine the second pair of congruent angles.

Statements
Reasons
1.
MS ∥ RQ
1.
Given
2.
∠ PMS ≅ ∠ PRQ
2.
Alternate Interior Angles Theorem
3.
∠ SPM ≅ ∠ QPR
3.
Vertical Angles Theorem
4.
MS ≅ RQ
4.
Given
5.
△ MSP ≅ △ RQP
5.
Angle-Angle-Side (AAS) Congruence Postulate
Practice makes perfect

We begin by noticing that ∠ SPM and ∠ QPR are vertical angles, and so by the Vertical Angles Theorem we conclude that ∠ SPM ≅ ∠ QPR.

Since MS ∥ RQ and MR is a transversal, by the Alternate Interior Angles Theorem we get that ∠ PMS ≅ ∠ PRQ.

Remember that we also have MS ≅ RQ, and so by applying the Angle-Angle-Side (AAS) Congruence Postulate we get △ MSP ≅ △ RQP. We summarize this proof in the following two-column table.

Statements
Reasons
1.
MS ∥ RQ
1.
Given
2.
∠ PMS ≅ ∠ PRQ
2.
Alternate Interior Angles Theorem
3.
∠ SPM ≅ ∠ QPR
3.
Vertical Angles Theorem
4.
MS ≅ RQ
4.
Given
5.
△ MSP ≅ △ RQP
5.
Angle-Angle-Side (AAS) Congruence Postulate
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arrow_right Exercises p.367-371
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Exercises 2 (Page 367)
Exercises 3 (Page 367)
Exercises 4 (Page 367)
Exercises 5 (Page 368)
Exercises 6 (Page 368)
Exercises 7 (Page 368)
Exercises 8 (Page 368)
Exercises 9 (Page 368)
Exercises 10 (Page 368)
Exercises 11 (Page 368)
Exercises 12 (Page 369)
Exercises 13 (Page 369)
Exercises 14 (Page 369)
Exercises 15 (Page 369)
Exercises 16 (Page 369)
Exercises 17 (Page 370)
Exercises 18 (Page 370)
Exercises 19 (Page 370)
Exercises 20 (Page 370)
Exercises 21 (Page 370)
Exercises 22 (Page 370)
Exercises 23 (Page 370)
Exercises 24 (Page 370)
Exercises 25 (Page 370)
Exercises 26 (Page 370)
Exercises 27 (Page 371)
Exercises 28 (Page 371)
Exercises 29 (Page 371)
Exercises 30 (Page 371)
Exercises 31 (Page 371)
Exercises 32 (Page 371)
Exercises 33 (Page 371)
34 engineering
35 engineering
36 engineering
Exercises 37 (Page 371)
Exercises 38 (Page 371)