Geometry Quiz: Angle Pairs Basics

📐 A 5-Item Multiple Choice Quiz on Angle Pairs

As you embark on your geometry journey, let's test your understanding of some fundamental angle pair concepts by taking a quiz. We'll focus on complementary angles, supplementary angles, vertical angles, adjacent angles, and linear pairs.

🔹 Complementary Angles

Question 1: Which pair of angles, whose sum is always (90^\circ), are called complementary angles?

A) Two angles that share a vertex and are on opposite sides of a transversal line B) Two angles that have different measures but add up to (90^\circ) C) Two angles of a straight line D) Two angles with the same measure that add up to (180^\circ)

Answer: B) Two angles that have different measures but add up to (90^\circ)

Example: Angle A and Angle B in the right triangle are complementary since (m\angle A + m\angle B = 90^\circ).

🔶 Supplementary Angles

Question 2: Two angles that add up to (180^\circ) are called supplementary angles.

A) False B) True

Answer: B) True

Example: If Angle A and Angle B are interior angles of a straight line, then they are supplementary.

🟣 Vertical Angles

Question 3: Two non-adjacent angles that form a linear pair are called vertical angles.

A) True B) True

Answer: A) True

Example: In the figure, if line m and line n intersect at point P, then (\angle 1) and (\angle 3) are vertical angles, as are (\angle 2) and (\angle 4).

🟦 Adjacent Angles

Question 4: Two angles whose vertices lie on the same ray, called a transversal, and share a side are called adjacent angles.

A) True B) True

Answer: A) True

Example: In the figure, if line m and line n intersect at point P, then (\angle 1) and (\angle 2) are adjacent angles.

🟩 Linear Pairs

Question 5: A set of four angles formed when a transversal intersects two parallel lines is called a linear pair.

A) True B) True

Answer: A) True

Example: In the figure, when line m intersects parallel lines n and p at points Q and R, the four angles formed are a linear pair.

📝 Review

In the quiz, we explored the following concepts related to angle pairs:

1. Complementary angles: Two angles with different measures that add up to (90^\circ).
2. Supplementary angles: Two angles that add up to (180^\circ).
3. Vertical angles: Two non-adjacent angles that form a linear pair.
4. Adjacent angles: Two angles whose vertices lie on the same ray and share a side.
5. Linear pairs: A set of four angles formed when a transversal intersects two parallel lines.

Understanding these angle pair concepts is essential in the study of geometry, as they form the foundation for theorems and theorems-in-proofs that follow. So now that you've worked through this quiz, you're well on your way to mastering these fundamental ideas!