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Difficulty: EasyLines and Angles

A drafter is reviewing a set of architectural plans. Connect each described geometric condition with its correct mathematical term.

  • Two angles whose sum is exactly 180∘180^\circSupplementary angles
  • Two angles whose sum is exactly 90∘90^\circComplementary angles
  • A pair of opposite, equal angles formed by two intersecting linesVertical angles
  • Two straight lines that intersect to form a right anglePerpendicular lines

Answer

Two angles summing to 180∘180^\circ match with Supplementary angles; two angles summing to 90∘90^\circ match with Complementary angles; opposite equal angles match with Vertical angles; lines forming a right angle match with Perpendicular lines.
Each definition precisely matches the fundamental geometric axioms for angles and lines. Recognizing these definitions is essential for solving more complex geometry problems.

Step-by-Step Solution

1
Identify the geometric term for two angles whose sum is exactly 180∘180^\circ.
Supplementary angles
By geometric definition, a pair of angles that add up to 180∘180^\circ (forming a straight line if adjacent) are supplementary.
2
Identify the geometric term for two angles whose sum is exactly 90∘90^\circ.
Complementary angles
By geometric definition, a pair of angles that add up to 90∘90^\circ (forming a right angle if adjacent) are complementary.
3
Identify the term for the opposite angles created when two lines intersect.
Vertical angles
Intersecting lines create two pairs of non-adjacent, opposite angles known as vertical angles, which are congruent.
4
Identify the term for straight lines that intersect to form a right angle.
Perpendicular lines
When lines intersect at exactly 90∘90^\circ, they are defined mathematically as perpendicular.

Key Concept

Basic terminology for angle relationships and line intersections
Estimated Time:45s
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Topics

Lines and Angles

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