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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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Exercise 23 Page 395

Use the Alternate Interior Angles Theorem and look for a pair of vertical angles.

Statements
Reasons
1.
AB∥ DC and AB ≅ DC
1.
Given
2.
∠ ABE ≅ ∠ CDE
2.
Alternate Interior Angles Theorem
3.
∠ BEA ≅ ∠ DEC
3.
Vertical Angles Theorem
4.
△ ABE ≅ △ CDE
4.
Angle-Angle-Side (AAS) Congruence Postulate
Practice makes perfect
Since AB ∥ DC and BD is a transversal, by the Alternate Interior Angles Theorem we get that ∠ ABE ≅ ∠ CDE. Additionally, we are told that AB ≅ CD.

Notice that ∠ BEA ≅ ∠ DEC since they are vertical angles. Therefore, by the Angle-Angle-Side (AAS) Congruence Postulate we get that △ ABE ≅ △ CDE.

Two-Column Proof Table

In the following table we summarize the proof we did before.

Statements
Reasons
1.
AB∥ DC and AB ≅ DC
1.
Given
2.
∠ ABE ≅ ∠ CDE
2.
Alternate Interior Angles Theorem
3.
∠ BEA ≅ ∠ DEC
3.
Vertical Angles Theorem
4.
△ ABE ≅ △ CDE
4.
Angle-Angle-Side (AAS) Congruence Postulate
Subchapter links expand_more
arrow_right 1 Angles of Triangles p.394
11
Angles of Triangles 12 (Page 394)
Angles of Triangles 13 (Page 394)
Angles of Triangles 14 (Page 394)
arrow_right 2 Congruent Triangles p.394
Congruent Triangles 15 (Page 394)
Congruent Triangles 16 (Page 394)
Congruent Triangles 17 (Page 394)
arrow_right 3 Proving Triangles Congruent-SSS, SAS p.395
Proving Triangles Congruent-SSS, SAS 18 (Page 395)
Proving Triangles Congruent-SSS, SAS 19 (Page 395)
Proving Triangles Congruent-SSS, SAS 20 (Page 395)
Proving Triangles Congruent-SSS, SAS 21 (Page 395)
Proving Triangles Congruent-SSS, SAS 22 (Page 395)
arrow_right 4 Proving Triangles Congruent-ASA, AAS p.395
Proving Triangles Congruent-ASA, AAS 23 (Page 395)
Proving Triangles Congruent-ASA, AAS 24 (Page 395)
arrow_right 5 Isosceles and Equilateral Triangles p.396
Isosceles and Equilateral Triangles 25 (Page 396)
Isosceles and Equilateral Triangles 26 (Page 396)
Isosceles and Equilateral Triangles 27 (Page 396)
arrow_right 6 Triangles and Coordinate Proof p.396
Triangles and Coordinate Proof 28 (Page 396)
Triangles and Coordinate Proof 29 (Page 396)
Triangles and Coordinate Proof 30 (Page 396)