25. Proof Write a two-column proof to prove the Same-Side Interior Angles Theorem (Theorem 3-2).

    Given: l || m l vertical linevertical line m

    Prove: ∠ 3 angle 3  and ∠ 6 angle 6  are supplementary.

26. Proof Write a two-column proof.

    Given: a || b , ∠ 1 ≅ ∠ 4 eh vertical linevertical line b comma angle 1 approximately equal to angle 4

    Prove: ∠ 2 ≅ ∠ 3 angle 2 approximately equal to angle 3

    
    Image Long Description

C Challenge

Use the diagram below for Exercises 27 and 28.

Image Long Description

27. Algebra Suppose the measures of ∠ 1 angle 1  and ∠ 2 angle 2  are in a 4 : 11 ratio. Find their measures. (Diagram is not to scale.)
28. Error Analysis The diagram contains contradictory information. What is it? Why is it contradictory?

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

29. ∠ 1 angle 1  and ∠ 2 angle 2  are same-side interior angles formed by two parallel lines and a transversal. If m ∠ 1 = 115 , m angle . 1 equals 115 comma  what is m ∠ 2 ? m angle 2 question mark

30. The rectangular swimming pool shown below has an area of 1500   ft 2 . 1500 , , ft squared , .  A rectangular walkway surrounds the pool. How many feet of fencing do you need to surround the walkway?

    

31. The measure of an angle is two times the measure of its complement. What is the measure of the angle?
32. ∠ 1 angle 1  and ∠ 2 angle 2  are vertical angles. If m ∠ 1 = 4 x m angle , 1 equals 4 x  and m ∠ 2 = 56 , m angle . 2 equals 56 comma  what is the value of x?

Mixed Review

See Lesson 3-1.

Determine whether each statement is always, sometimes, or never true.

33. Skew lines are coplanar.
34. Skew lines intersect.
35. Parallel planes intersect.
36. Rays are parallel.

See Lesson 2-2.

Get Ready! To prepare for Lesson 3-3, do Exercises 37–39.

Write the converse and determine its truth value.

37. If a triangle is a right triangle, then it has a 90 ° 90 degrees  angle.
38. If two angles are vertical angles, then they are congruent.
39. If two angles are same-side interior angles, then they are supplementary.

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