The postulate and three theorems you have just learned provide you with four ways to determine if two lines are parallel.
Problem 3 Determining Whether Lines are Parallel
The fence gate below is made up of pieces of wood arranged in various directions. Suppose
Explain.
Think
How do
Yes,
✓ Got It?
- In Problem 3, what is another way to explain why
You can use algebra along with the postulates and theorems from Lesson 3-2 and Lesson 3-3 to help you solve problems involving parallel lines.
Problem 4 Using Algebra
Algebra What is the value of x for which
The two angles are same-side interior angles. By the Converse of the Same-Side Interior Angles Theorem,
Think
Work backward. Think about what must be true of the given angles for a and b to be parallel.
✓ Got It?
-
What is the value of w for which
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs