Two triangles share a common vertex where their sides intersect, forming a bowtie shape. Which theorem justifies that the angles at the shared vertex are congruent?

Alternate Interior Angles Theorem

Ray $\overrightarrow{QS}$ bisects $\angle PQR$. Which of the following statements is correct?

$\angle PQS$ and $\angle SQR$ are supplementary

Angle Relationships and Parallel Lines Practice — Grade 8 math

Lesson 7-1: Angle Relationships and Parallel Lines — Practice Questions

1. Two triangles share a common vertex where their sides intersect, forming a bowtie shape. Which theorem justifies that the angles at the shared vertex are congruent?
- A. Alternate Interior Angles Theorem
- B. Vertical Angles Theorem
- C. Angle Bisector Theorem
- D. Corresponding Angles Theorem
2. In a figure, $\overline{PQ} \parallel \overline{RS}$ and a transversal cuts through both lines forming a Z-shape. Which pair of angles are congruent?
- A. Corresponding angles
- B. Supplementary angles
- C. Alternate interior angles
- D. Vertical angles
3. Ray $\overrightarrow{QS}$ bisects $\angle PQR$. Which of the following statements is correct?
- A. $\angle PQS > \angle SQR$
- B. $\angle PQS \cong \angle SQR$
- C. $\angle PQR \cong \angle SQR$
- D. $\angle PQS$ and $\angle SQR$ are supplementary
4. In a proof, lines $\overline{AC}$ and $\overline{BD}$ intersect at point $E$. To justify that $\angle AEB \cong \angle CED$, you would use the ___ Angles Theorem.
5. To prove $\triangle ABD \cong \triangle CBD$ using ASA, you are given $\angle A \cong \angle C$ and $\overline{BD}$ bisects $\angle ABC$. What is the second pair of congruent angles needed?
- A. $\angle ADB \cong \angle CDB$
- B. $\angle ABD \cong \angle CBD$
- C. $\angle BAD \cong \angle BCD$
- D. $\angle ADB \cong \angle ABC$
6. Two vertical fence posts are installed to be parallel. If the distance between the posts at the bottom is 4 feet, the distance between them at the top must be ___ feet.
7. Which statement best describes two parallel lines?
- A. They cross at one point.
- B. They are always the same distance apart.
- C. They form a 90-degree angle.
- D. They can be curved.
8. Line $\overleftrightarrow{MN}$ is parallel to line $\overleftrightarrow{PQ}$. Which statement correctly uses mathematical symbols to represent this fact?
- A. $\overleftrightarrow{MN} \perp \overleftrightarrow{PQ}$
- B. $\overleftrightarrow{MN} = \overleftrightarrow{PQ}$
- C. $\overleftrightarrow{MN} \parallel \overleftrightarrow{PQ}$
- D. $\overleftrightarrow{MN} > \overleftrightarrow{PQ}$
9. In a notebook, the top line and the fifth line are parallel. The distance between them on the left side of the page is 10 cm. What is the distance between them on the right side? ___ cm.
10. Which of the following is the best example of a pair of parallel lines?
- A. The hands of a clock at 3:00.
- B. Two adjacent sides of a square.
- C. The two rails of a straight train track.
- D. The letter X.