The Equation practice with congruent angles exercise appears under the 8th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise uses congruent and supplementary angles with parallel lines to practice setting up and solving linear equations.
Types of Problems
There are two types of problems in this exercise:
- Use the congruent angles to find the variable: This problem provides a picture with two parallel lines and a transversal. Two congruent angles are described with variables and users are expected to find the value of the variable.
- Use the supplementary angles to find the variable: This problem provides a picture with two parallel lines and a transversal. Two supplementary angles are described with variables and the user is expected to find the value of the variable.
Strategies
Knowledge of some of the angles theorems and postulates are helpful and an ability to solve linear equations is necessary for success on this exercise.
- The angles that are congruent to a given angle are called corresponding, alternate interior, alternate exterior and vertical.
- The angles that are supplementary to a given angle are those that form a linear pair, same-side interior, or same-side exterior.
- 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
- The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and the planes, they had to use geometry to measure their gardens and fields all over again.
- Many geometric concepts come up in the fields of architecture and graphical design.
- Engineers and architects use angles for designs, roads, buildings and sporting facilities.
- Athletes use angles to enhance their performance.
- Carpenters use angles to make chairs, tables and sofas.
- Artists use their knowledge of angles to sketch portraits and paintings.