103r. Review Angles in Parallel Lines

Learning Intentions

• To understand that parallel lines do not cross and that arrows are used to indicate this on a diagram
• To know the meaning of the terms transversal, corresponding, alternate and co-interior
• Use properties of parallel lines to Solve unknown angles

Pre-requisite Summary

• Know that an angle measures the amount of turn between two lines
• Recall that angles are measured in degrees, written as
• Know that angles on a straight line add to
• Know that angles at a point add to
• Understand that vertically opposite angles are equal
• Know that perpendicular lines meet at
• Be able to Identify when two lines cross
• Be familiar with angle facts used to find unknown angles

Worked Examples

Worked Example 1

State the meaning of each term:

a) parallel lines

b) transversal

c) corresponding angles

Worked Example 2

State the meaning of each term:

a) alternate angles

b) co-interior angles

c) arrows on a diagram showing parallel lines

Worked Example 3

Two parallel lines are cut by a transversal. One angle is . Find:

a) the corresponding angle

b) an alternate angle

c) the co-interior angle on the same side of the transversal

Worked Example 4

Two parallel lines are cut by a transversal. One angle is . Find:

a) the corresponding angle

b) an alternate angle

c) the co-interior angle

Worked Example 5

Find the unknown angle:

a) Corresponding angles are and

b) Alternate angles are and

c) Co-interior angles are and

Worked Example 6

Use properties of parallel lines to find each unknown angle:

a) One angle is and its co-interior partner is

b) One angle is and its corresponding angle is

c) One angle is and its alternate angle is

Problems

Problem 1

State the meaning of each term:

a) parallel lines

b) transversal

c) corresponding angles

Problem 2

State the meaning of each term:

a) alternate angles

b) co-interior angles

c) arrows on a diagram showing parallel lines

Problem 3

Two parallel lines are cut by a transversal. One angle is . Find:

a) the corresponding angle

b) an alternate angle

c) the co-interior angle on the same side of the transversal

Problem 4

Two parallel lines are cut by a transversal. One angle is . Find:

a) the corresponding angle

b) an alternate angle

c) the co-interior angle

Problem 5

Find the unknown angle:

a) Corresponding angles are and

b) Alternate angles are and

c) Co-interior angles are and

Problem 6

Use properties of parallel lines to find each unknown angle:

a) One angle is and its co-interior partner is

b) One angle is and its corresponding angle is

c) One angle is and its alternate angle is

Exercises

Understanding and Fluency

Exercise 1.

State the meaning of each term:

a) parallel lines

b) transversal

c) corresponding angles

d) alternate angles

Exercise 2.

State the meaning of each term:

a) co-interior angles

b) arrows on a diagram

c) same side of a transversal

Exercise 3.

Decide whether each statement is true or false:

a) Parallel lines cross if extended far enough

b) A transversal cuts across two or more lines

c) Corresponding angles in parallel lines are equal

d) Co-interior angles in parallel lines add to

Exercise 4.

One angle formed by a transversal across parallel lines is . Find:

a) a corresponding angle

b) an alternate angle

c) a co-interior angle

Exercise 5.

One angle formed by a transversal across parallel lines is . Find:

a) a corresponding angle

b) an alternate angle

c) a co-interior angle

Exercise 6.

Find each unknown angle:

a) Corresponding angles are and

b) Alternate angles are and

c) Co-interior angles are and

Exercise 7.

Find each unknown angle:

a) Corresponding angles are and

b) Alternate angles are and

c) Co-interior angles are and

Exercise 8.

Use angle properties to find each unknown:

a)

b) because it is corresponding to an angle of

c) because it is alternate to an angle of

Reasoning

Exercise 9.

Explain why corresponding angles are equal when a transversal cuts parallel lines.

Exercise 10.

A student says that co-interior angles are always equal. Explain the mistake.

Exercise 11.

Noah says that alternate angles add to . Is he correct? Explain.

Exercise 12.

Explain why arrows are useful on a diagram with parallel lines.

Exercise 13.

A student sees two equal angles and assumes they must be corresponding angles. Describe why this may not always be true.

Problem-solving

Exercise 14.

Two parallel roads are crossed by another road. One angle formed is . Find the angle in the corresponding position at the second road crossing.

Exercise 15.

A railway line crosses two parallel streets. One interior angle is . Find the co-interior angle on the same side of the transversal.

Exercise 16.

In a diagram, two parallel lines are cut by a transversal. An angle is marked and its alternate angle is . Find .

Exercise 17.

A builder marks two fence rails as parallel Use arrows. A support beam crosses both rails. One angle formed is . Find an alternate angle and a co-interior angle.

Exercise 18.

A student is told that two angles on the same side of a transversal inside parallel lines are co-interior. One angle is . Find the other.

Exercise 19.

In a parallel line diagram, one angle is . List the sizes of all other distinct angle values that can appear in the diagram.

Potential Misunderstandings

• Students may think parallel lines eventually cross if the diagram is extended
• Students may ignore the arrow markings that show lines are parallel
• Students may confuse a transversal with a parallel line
• Students may mix up corresponding and alternate angles
• Students may think co-interior angles are equal instead of supplementary
• Students may forget that co-interior angles add to
• Students may use the wrong angle pair when finding an unknown angle
• Students may assume angle rules for parallel lines Apply even when the lines are not marked parallel
• Students may confuse the position of angles inside and outside the parallel lines
• Students may rely on the appearance of a diagram instead of the stated angle properties
• Students may think any equal angles in the diagram must be corresponding
• Students may forget to use straight-line or vertically opposite angle facts together with parallel line properties

Next: 104r. Reviewing Classifying Triangles and Finding Angles