Geometry Word Problems Study Guide
Find practice problems and solutions for these concepts at Geometry Word Problems Practice Problems.
While probability problems are usually word problems, geometry problems usually have a diagram. They can be a bit tougher when there are no pictures, just words, to describe a shape and its dimensions. We can use the eight-step process to solve a geometry problem, but often it's better to draw a picture. Sometimes, we may even want to do both.
Angles: Subject Review
When two parallel lines are cut by a transversal, adjacent angles, corresponding angles, vertical angles, and supplementary angles are created. Corresponding angles, or alternating angles, are congruent to each other, as are vertical angles.
Fuel for Thought
Adjacent angles are two angles that are next to each other, sharing a vertex and a side.
A vertex is the point where two rays or lines meet to form an angle.
If two angles, lines, or shapes are equal in measure, then they are congruent.
Corresponding angles are two or more congruent angles that have similar positions in a shape or figure.
Vertical angles are congruent angles that are formed by the intersection of two lines. Vertical angles are opposite to each other, which is why they are sometimes called opposite angles.
Supplementary angles are two angles whose measures total 180°.
A diagram or shape can also contain acute, obtuse, or right angles. Two right angles are complementary to each other.
Fuel for Thought
A triangle is a three-sided polygon whose angles total 180°.
An acute angle measures less than 90°. At least two angles in a triangle are acute. If all three angles are less than 90°, then the triangle is an acute triangle.
A right angle measures exactly 90°. No more than one angle in a triangle can be a right angle. If a triangle does contain a 90° angle, then it is a right triangle.
An obtuse angle measures greater than 90°. No more than one angle in a triangle can be an obtuse angle. If a triangle does contain an angle that is greater than 90°, then it is an obtuse triangle.
Complementary angles are two angles whose measures total 90°.
An equilateral triangle has three congruent sides and three congruent, 60° angles.
An isosceles triangle has two congruent sides and two congruent angles.
When we are working on an angle word problem where one single angle measure is given and we are looking for the measure of another angle, it's likely our answer will be either (1) the same measure as the angle given, (2) the complement of the given angle, or (3) the supplement of the given angle. The keywords corresponding, alternating, and vertical can signal that two angles are congruent. The keyword supplementary can mean that we must subtract the measure of one angle from 180°, and the keyword complementary can indicate that we must subtract the measure of one angle from 90°.
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