Foundations of Euclidean Geometry — Test

Question 7 • Geometry

In which diagram do angles 1 and 2 form a linear pair?

Answer

Image with description Two lines intersect at a point, forming four angles. Angle 1 is on the left side of the intersection, and angle 2 is on the right side of the intersection.

Image with description A horizontal line passes through a point. Two rays extend upward from the point, one to the upper left and one to the upper right. Angle 1 is between the left side of the horizontal line and the upper-left ray. Angle 2 is between the two upward rays. Angle 3 is between the upper-right ray and the right side of the horizontal line.

Image with description A ray extends upward and to the right from a point on a horizontal line. Angle 1 is between the left side of the horizontal line and the ray. Angle 2 is between the ray and the right side of the horizontal line.

Image with description Three rays extend from the same point. One ray extends horizontally to the left, one extends vertically downward, and one extends diagonally downward to the left. A right-angle marker is shown between the horizontal and vertical rays. Angle 1 is between the horizontal ray and the diagonal ray. Angle 2 is between the diagonal ray and the vertical ray.

Explanation

A linear pair consists of two adjacent angles whose noncommon sides are opposite rays, forming a straight line. In diagram A, angles 1 and 2 share the upward-right ray, and their other sides point in opposite directions along the horizontal line. In B, angles 1 and 2 are opposite rather than adjacent, so they do not form a linear pair.

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