Lines and Angles

Geometry

Lesson by Mike McGarry

Magoosh Expert

Lesson by Mike McGarry

Magoosh Expert

Summary

Geometry on the ACT begins with a few foundational ideas: lines, segments, angles, and the relationships created when shapes are bisected or when lines intersect. Success depends on understanding exact geometric definitions, avoiding visual assumptions, and using a few reliable angle rules to solve problems efficiently.

Geometry studies shapes, and the best way to strengthen understanding is to actively draw figures and build them with physical objects so visual and spatial relationships become easier to recognize.
A line extends forever in both directions, while a line segment has endpoints; straight does not mean horizontal, and a figure that looks horizontal, vertical, or perpendicular cannot be assumed to be so unless the test explicitly indicates it.
Angles measure turning in degrees, can be named with the vertex in the middle, and rely on basic facts such as 180 degrees in a straight angle and 90 degrees in a right angle; perpendicular lines meet at right angles, but that relationship must be stated, not guessed from appearance.
Congruent figures have the same shape and size, and bisectors split a shape into two congruent parts; an angle bisector creates two equal angles, a segment bisector creates two equal halves, and a perpendicular bisector also identifies points equidistant from a segment’s endpoints.
Angles on a straight line are supplementary and sum to 180 degrees, while vertical angles formed by intersecting lines are congruent, allowing one known angle to determine the others around an intersection.
Parallel lines cut by a transversal create eight angles where all large angles are equal, all small angles are equal, and any large angle plus any small angle equals 180 degrees, making it possible to find every angle from just one given measure.

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