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Questions and Answers
What defines complementary angles?
In the context of angles, what do vertical angles refer to?
Which statement correctly describes supplementary angles?
What differentiates adjacent angles from vertical angles?
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How are linear pairs distinguished from complementary pairs?
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What type of triangle has one angle greater than 90° and the other two angles less than 90°?
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In a right triangle, what is the measure of the third angle if one of the acute angles measures 45°?
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Which type of triangle has all three sides of different lengths?
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What are the measures of angles in an equilateral triangle?
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If all angles in a triangle are less than 90°, what type of triangle is it?
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Study Notes
📐 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:
- Complementary angles: Two angles with different measures that add up to (90^\circ).
- Supplementary angles: Two angles that add up to (180^\circ).
- Vertical angles: Two non-adjacent angles that form a linear pair.
- Adjacent angles: Two angles whose vertices lie on the same ray and share a side.
- 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!
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Description
Test your knowledge of fundamental angle pair concepts with this 5-item multiple-choice quiz! Explore complementary angles, supplementary angles, vertical angles, adjacent angles, and linear pairs. Mastering these concepts is essential for understanding geometric theorems and proofs.
