Under which condition are corresponding angles, formed by a transversal intersecting two lines, guaranteed to be congruent?

When the transversal is perpendicular to the lines

When the two lines are parallel

When the two lines are perpendicular

Understand Angle Relationships and Parallel Lines Practice — Grade 7 math

Lesson 11-3: Understand Angle Relationships and Parallel Lines — Practice Questions

1. Two parallel lines are intersected by a transversal. The angle in the bottom-right position at one intersection is $82^\circ$. What is the measure of the corresponding angle at the other intersection?
- A. $8^\circ$
- B. $82^\circ$
- C. $98^\circ$
- D. $180^\circ$
2. Lines $p$ and $q$ are parallel and cut by a transversal. Two corresponding angles measure $(3x + 15)^\circ$ and $(5x - 5)^\circ$. What is the value of $x$? The value of $x$ is ___.
3. A transversal intersects two parallel lines, forming corresponding angles with measures of $(2y + 50)^\circ$ and $(4y + 20)^\circ$. What is the measure of these angles in degrees? The measure is ___ degrees.
4. Two parallel lines are cut by a transversal. An angle measures $105^\circ$. What is the measure of an angle supplementary to its corresponding angle?
- A. $75^\circ$
- B. $105^\circ$
- C. $180^\circ$
- D. $255^\circ$
5. Under which condition are corresponding angles, formed by a transversal intersecting two lines, guaranteed to be congruent?
- A. When the transversal is perpendicular to the lines
- B. When the two lines are parallel
- C. When the two lines are perpendicular
- D. They are always congruent
6. A transversal intersects two other lines at two distinct points. How many angles are created by these intersections? ___
7. Which of the following statements correctly defines a transversal?
- A. A line that intersects two or more other lines at distinct points.
- B. A line that is parallel to another line.
- C. A line that intersects another line at exactly one point.
- D. A line that creates four right angles at an intersection.
8. For a line to be called a transversal, it must intersect a minimum of ___ other lines.
9. Line $p$ intersects line $q$ at point A and line $r$ at point B. Which line acts as the transversal?
- A. Line $p$
- B. Line $q$
- C. Line $r$
- D. No line is a transversal.
10. If three lines $a$, $b$, and $c$ all intersect at the same single point, can line $a$ be a transversal to lines $b$ and $c$?
- A. Yes, because it crosses two lines.
- B. No, because the intersection points must be distinct.
- C. Yes, because three lines are present.
- D. No, because the lines are not parallel.