Question

geo lesson 2.5 homework

1. based on the figure shown, fill in the blanks to make the statements true.

a. angle a and angle ___ are corresponding angles.
b. angle b and angle ___ are alternate exterior angles.
c. angle c and angle ___ are alternate interior angles.
d. angle d and angle ___ are corresponding interior angles.
e. angle f and angle ___ are supplementary angles.
f. angle g and angle ___ are vertical angles.

1. draw parallel lines and a transversal to scale such that a pair of corresponding angles are each 62°. label the measures of the corresponding angles on your figure.

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal:

• Corresponding angles are in the same relative position.
• Alternate interior angles are between the two parallel lines and on opposite sides of the transversal.
• Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal.
• Vertical angles are opposite each other when two lines intersect.
• Supplementary angles add up to 180 degrees.

For the given figure with parallel lines and a transversal:
a. Angle A and angle D are corresponding angles.
b. Angle B and angle G are alternate exterior angles.
c. Angle C and angle F are alternate interior angles.
d. Angle D and angle E are not mentioned in the problem - but if we assume a full - turn around the intersection, we focus on the given relationships.
e. Angle G and angle F are vertical angles.

1.
a. Angle A and angle D are corresponding angles.
b. Angle B and angle G are alternate exterior angles.
c. Angle C and angle F are alternate interior angles.
d. There is no such angle E in the problem setup related to the given main angle - pair relationships.
e. Angle G and angle F are vertical angles.

1. To draw parallel lines and a transversal such that a pair of corresponding angles are each 62°:

• Draw two parallel lines.
• Draw a transversal that intersects the two parallel lines.
• At one of the intersection points, measure and mark an angle of 62°.
• Since corresponding angles are equal when two parallel lines are cut by a transversal, the corresponding angle at the other intersection will also be 62°.

Answer:

1.
a. corresponding
b. alternate exterior
c. alternate interior
d. N/A
e. vertical

1. Draw two parallel lines, then a transversal. Mark a 62 - degree angle at one intersection, and its corresponding angle at the other intersection will also be 62°.