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Geometry Course
More About Angles - Part 5
 Free Geometry Online Course •Part 1  Terms in Geometry •Part 2  Types of Angles •Part 3•Postulates • Part 4• Measuring Angles • Part 5 • More On Angles • Geometry Help • Conic Sections • Pythagorean Theorem
 Related Resources • Measurement Formulas • Recommended Resources • Area Calculator • Introduction to Polygons

1. Congruent angles are angles that have the same number of degrees. For instance, 2 line segments are congurent if they are the same in length. If two angles have the same measure, they too are considered congruent. Symbolically, this can be shown by: as

@
means that Line Segment AB is congruent to line segment OP

2. Bisectors refers to the line, ray or line segment that passes through the midpoint. The bisector divides a segment into two congruent setments as demonstrated here:

A ray that is in the interior of an angle and divides the original angle into two congruent angles is the bisector of that angle.

3. Exterior and Interior Angles

4. Transversal

A Transversal is a line that crosses two parallel lines. In the figure below, A and B are parallel lines. Note the following when a transversal cuts two parallel lines:

*the four acute angles will be equal
*the four obtuse angles will also be equal
*each acute angle is supplementary to eacy obtuse angle

5. 3 Theorems to Know - Especially for your SATs!

1. The sum of the measures of triangles always equals 180°. You can prove this by using your protractor to measure the three angles, then total the three angles. See triangle below - 90° + 45° + 45° = 180

2. The measure of the exterior angle will always equal the sum of the measure of the 2 remote interior angles. NOTE: the remote angles in the figure below are b and c. Therefore, the measure of RAB will be equal to the sum of B and C. If you know the measures B and C then you automatically know what RAB is!

3. If a transversal intersects two lines such that corresponding angles are congruent, then the lines are parallel. AND, If two lines are intersected by a transversal such that interior angles on the same side of the transversal are supplementary, then the lines are parallel. (See above Transversal)

Deb Russell
Mathematics Guide

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