Test questions for identifying and relating same-side interior angles

📚 Quick Study Guide

• 📐 Definition: Same-side interior angles are pairs of angles that lie on the same side of a transversal and between the two lines it intersects.
• 🧭 Location: They are located on the *inside* of the two lines, and on the *same side* of the transversal.
• ➕ Supplementary Property: If the two lines intersected by the transversal are parallel, then same-side interior angles are supplementary (their measures add up to $180^{\circ}$).
• ✍️ Symbolic Representation: If $\angle 1$ and $\angle 2$ are same-side interior angles and the lines are parallel, then $m\angle 1 + m\angle 2 = 180^{\circ}$.
• 💡 Identifying Transversals: The transversal is the line that cuts across the other two lines. Identifying it correctly is key!

✍️ Practice Quiz

1. What is the relationship between same-side interior angles when the lines they intersect are parallel?
   1. Alternate interior angles
   2. Corresponding angles
   3. Supplementary
   4. Complementary


2. If one of the same-side interior angles measures $60^{\circ}$ and the lines are parallel, what is the measure of the other angle?
   1. $30^{\circ}$
   2. $60^{\circ}$
   3. $90^{\circ}$
   4. $120^{\circ}$


3. Which of the following is NOT a characteristic of same-side interior angles?
   1. They lie on the same side of the transversal.
   2. They lie between the two lines.
   3. They are always congruent.
   4. They are supplementary when lines are parallel.


4. In a diagram with two parallel lines cut by a transversal, if one same-side interior angle is $x$ and the other is $2x$, what is the value of $x$?
   1. $30^{\circ}$
   2. $45^{\circ}$
   3. $60^{\circ}$
   4. $90^{\circ}$


5. What is the name given to the line that intersects two or more other lines?
   1. Parallel line
   2. Perpendicular line
   3. Transversal
   4. Angle bisector


6. If two lines are cut by a transversal and the same-side interior angles are NOT supplementary, what can you conclude?
   1. The lines are parallel.
   2. The lines are perpendicular.
   3. The lines are skew.
   4. The lines are not parallel.


7. Which pair of angles are same-side interior angles?
   1. Angles 1 and 5
   2. Angles 3 and 6
   3. Angles 2 and 7
   4. Angles 4 and 8