Question

1. from the picture on the left:

drag and drop each pair of angles
under a true statement. (many can be
placed under more than one true
statement or none of them.)
∠1 & ∠2
∠2 & ∠3
∠1 & ∠3
∠2 & ∠5
∠3 & ∠5
∠4 & ∠5
∠1 & ∠4
∠2 & ∠4
linear pair
answer by dragging items here
adjacent angles
answer by dragging items here
vertical angles
answer by dragging items here
congruent angles
answer by dragging items here
supplementary angles
answer by dragging items here
complimentary angles
answer by dragging items here

Explanation:

Step1: Recall definitions

• Linear Pair: Adjacent angles that sum to \(180^{\circ}\).
• Adjacent Angles: Share a common side and vertex.
• Vertical Angles: Opposite angles formed by two intersecting lines.
• Congruent Angles: Angles with equal measure.
• Supplementary Angles: Sum to \(180^{\circ}\).
• Complementary Angles: Sum to \(90^{\circ}\).

Step2: Analyze each pair

• \(\angle1\) & \(\angle2\):
• Adjacent (share side and vertex).
• Supplementary (\(\angle1 = 90^{\circ}\), \(\angle2=90^{\circ}\), \(90 + 90=180\)).
• \(\angle2\) & \(\angle3\):
• Linear Pair (adjacent, sum \(180^{\circ}\)).
• Supplementary.
• \(\angle1\) & \(\angle3\):
• Congruent (\(\angle1 = 90^{\circ}\), \(\angle3 = 90^{\circ}\)).
• \(\angle2\) & \(\angle5\):
• Congruent (vertical angles).
• \(\angle3\) & \(\angle5\):
• Adjacent.
• \(\angle4\) & \(\angle5\):
• Complementary (\(\angle1 = 90^{\circ}\), \(\angle4+\angle5=\angle1\)).
• Adjacent.
• \(\angle1\) & \(\angle4\):
• No specific relation.
• \(\angle2\) & \(\angle4\):
• No specific relation.

Answer:

• Linear Pair: \(\angle2\) & \(\angle3\)
• Adjacent Angles: \(\angle1\) & \(\angle2\), \(\angle3\) & \(\angle5\), \(\angle4\) & \(\angle5\)
• Vertical Angles: \(\angle2\) & \(\angle5\)
• Congruent Angles: \(\angle1\) & \(\angle3\), \(\angle2\) & \(\angle5\)
• Supplementary Angles: \(\angle1\) & \(\angle2\), \(\angle2\) & \(\angle3\)
• Complementary Angles: \(\angle4\) & \(\angle5\)