Pre Algebra Angle Relationships | Study Guide

University:
Virtual High School
Course:
STEM | Mathematics
Academic year:

2020
Views:

336

Pages:

6
Author:

Marilyn James

Angle Relationships Angle Relationships in Parallel Lines Crossed by a Transversal ● Corresponding Angles: pairs of angles in the same relative position on different parallels. ○ They are congruent . ● Alternate Interior Angles: pairs of angles on opposite sides of the transversal inside the parallel; they are congruent ○ In the image below, angles 4 and 6 are alternate interior angles, and so are 3 and 4 ● Alternate Exterior Angles: pairs of angles on opposite sides of the transversal outside the parallel lines; they are congruent. ○ In the image below, angles 2 and 8 are alternate exterior angles, and so are 1 and 7 ● Vertical Angles: Pairs of congruent angles. Formed when 2 lines intersect. T%he have sides that are opposite rays and share a vertex. ● Complementary Angles: Two angles whose sum is 90 degrees. ○ m∠1 + m∠2 = 90 degrees ● Supplementary Angles: Two angles whose sum is 180 degrees. ○ If they are adjacent, they form a linear pair ○ m∠1+ m∠2 = 180 degrees Angle Relationships in Basic Diagrams Example 1: ● Which angle is vertical to ∠AEC? ○ ∠DEB ● Which angle is vertical to ∠CEB? ○ ∠AED ● Name an angle that is supplementary to ∠AEC ○ ∠CEB ● If the m∠DEB is 35 degrees, what is m∠AEC? ○ 35 degrees ● If the m∠DEB is 35 degrees, what is the m∠AED? ○ 145 degrees Example 2: ● Find the measure of ∠IGH. ○ 90 - 50 = 40 degrees ● Find the measure of ∠IGF. ○ 180 - 50 = 130 degrees ● Which angle is complementary to ∠EGI? ○ ∠HGI Using Equations to Determine Angle Measurements ● What is the angle relationship? ○ Complementary ● Write and solve an equation based on the relationship between the angles. ○ m∠n = 18 degrees ; m∠(3n+18) = 72 degrees Angle Relationships in Triangles ● Triangle Sum Theorem: The sum of the three interior angles of a triangle equals 180°. ○ For triangle ABC: ∠A + ∠B + ∠C = 180 degrees ○ Example: Find ∠E ■ m∠E = 25 degrees ● Exterior Angle of a Triangle Theorem: ○ An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. ○ An exterior angle of a triangle has two remote interior angles. ■ A remote interior angle is an angle inside the triangle that is not adjacent to the exterior angle. ○ Exterior Angle Theorem: The measure of an exterior angle is equal to the sum of its two remote interior angles. ■ In the diagram above: m∠1+ m∠2= m∠4 Finding Angle Measures (in triangles) using Equations ● Find x (in the pic on the right)