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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 37 Page 371

Use the Transitive Property of Congruence and the Converse of Alternate Interior Angles Theorem.

Statements
Reasons
1.
∠ 2 ≅ ∠ 1 and ∠ 1 ≅ ∠ 3
1.
Given
2.
∠ 2 ≅ ∠ 3
2.
Transitive Property of Congruence
3.
∠ 2 and ∠ 3 are alternate interior angles
3.
From the diagram
4.
AB ∥ DE
4.
Converse of Alternate Interior Angles Theorem
Practice makes perfect
From the given diagram, we can see that BD is a transversal of AB and DE. This implies that ∠ 2 and ∠ 3 are alternate interior angles.

Since ∠ 2 ≅ ∠ 1 and ∠ 1 ≅ ∠ 3, by the Transitive Property of Congruence we get ∠ 2 ≅ ∠ 3. Next, by the Converse of Alternate Interior Angles Theorem we conclude that AB ∥ DE. We summarize this proof in the following table.

Statements
Reasons
1.
∠ 2 ≅ ∠ 1 and ∠ 1 ≅ ∠ 3
1.
Given
2.
∠ 2 ≅ ∠ 3
2.
Transitive Property of Congruence
3.
∠ 2 and ∠ 3 are alternate interior angles
3.
From the diagram
4.
AB ∥ DE
4.
Converse of Alternate Interior Angles Theorem
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arrow_right Exercises p.367-371
1
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)