Parallel lines 1

The  exercise appears under the 8th Grade Math Mission. This exercise introduces congruent and supplementary angles in diagrams with parallel lines.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the measure of the congruent angle: This problem provides a diagram with two angles that are congruent. One is given a measure and the student is asked to find the measure of the other.Pl1-1.png
 * 2) Find the measure of the supplementary angle: This problem provides a diagram with two angles that are supplementary. One is labeled with a measure and the student is asked to find the measure of the other one.Pl1-2.png

Strategies
Knowledge of some of the angles theorems and postulates are helpful on this exercise but the definitions of supplementary and congruent are more important.
 * 1) The angles that are congruent to a given angle are called corresponding, alternate interior, alternate exterior and vertical. They have equal measures.
 * 2) The angles that are supplementary to a given angle are those that form a linear pair, same-side interior, or same-side exterior. They have measures that sum to 180 degrees.
 * 3) The picture should make some angles look obtuse and some angles look acute. As long as there are parallel lines, the angles that look congruent are and angles that don't look congruent are supplementary.

Real-life applications

 * 1) Many geometric concepts come up in the fields of architecture and graphical design.