Unit 1, Lesson 14
Alternate Interior Angles
Grade 8
Practice
Problem 1
Use the diagram to find the measure of each angle.
- angle
- angle
- angle
A horizontal line and a line that slopes downward from left to right. The lines intersect at a point labeled B. On the horizontal line, point E is to the left of B and C is to the right of B. On the sloping line, point A is above B and point D is below B. Angle C B D is labeled 45 degrees.
Problem 2
Lines
Two parallel lines, k and l, cut by transversal line m. Points F, C and D are on line k. Points A and B are on line l. Points E, C and B are on transversal m. Angle E C F is marked congruent to angle D C B and to angle A B C.
- Explain why the measure of angle
is . If you get stuck, consider translating line by moving to . - What is the measure of angle
? Explain.
Problem 3
The diagram shows three lines with some marked angle measures:
Two lines that do not intersect. A third line intersects with both lines. At the first intersection, angles are marked starting at the top right and going in the clockwise direction, 70 degrees, question mark, question mark, question mark. At the second intersection, angles are marked starting at the top right and going in the clockwise direction, 53 degrees, question mark, question mark, question mark.
Find the missing angle measures marked with question marks.
Problem 4
Lines
Problem 5
from an earlier course
The two figures are scaled copies of each other.
Two identical quadrilaterals on a grid. In quadrilateral A C D, point A is 2 units right and 7 units up from the edge of the grid. Point D is 5 units right and 5 units up. Point C is 4 units right and 7 units up. A point, no labeled, but part of quadrilateral A C D is 5 units right and 8 units up. Quadrilateral A C D is labeled Figure 1. In quadrilateral P Q R S, point P is 8 units right and 8 units up. Point Q is 16 units right and 11 units up. Point R is 14 units right and 8 units up. Point S is 16 units right and 2 units up. Quadrilateral P Q R S is labeled Figure 2.
- What is the scale factor that takes Figure 1 to Figure 2?
- What is the scale factor that takes Figure 2 to Figure 1?