3.1 Review Worksheet (continued)
30. Complete the following two-column proof. Given: AB || CD , ∠ 1 ≅ ∠ 2, ∠ 3 ≅ ∠ 4 Prove: BC || DE
31. Edmund Dulac used perspective when drawing the floor tiles in this illustration for The Wind’s Tale by Hans Christian Andersen. Show that DJ || EK if m ∠ l = (3 x + 2) ° , m ∠ 2 = (5 x − 10) ° , and x = 6. A F G H J B C D 1
Proof:
2
Statements
Reasons
E
K
1. AB || CD 2. ∠ 1 ≅ ∠ 3
1. Given
2. a.
? ? ? ?
3. ∠ 1 ≅ ∠ 2, ∠ 3 ≅ ∠ 4 3. b.
4. c. 5. e.
4. ∠ 2 ≅ ∠ 4
5. d.
?
3.1.4 Properties of Perpendicular Lines 32. Name the shortest segment from point W to XZ.
X
Y
Z
x + 8
19
W
33. Write and solve an inequality for x .
157
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