8-4+Study+Guide


 * Lesson 8-4**

**ALGEBRA** **Quadrilateral //ABCD// is a rectangle.**
 * Example 1 Diagonals of a Rectangle**

The diagonals of a rectangle are congruent, so.
 * If //AC// = 4//x// - 13 and //BD// = 2//x// + 14, find //x//.**

Diagonals of a rectangle are. //AC// = //BD// Definition of congruent segments. 4//x// - 13 = 2//x// + 14 Substitution 2//x// - 13 = 14 Subtract 2//x// from each side. 2//x// = 27 Add 13 to each side. //x// = Divide each side by 2.


 * Example 2 Angles of a Rectangle**
 * ALGEBRA Quadrilateral //PQRS// is a rectangle.**

//QPS// is a right angle, so //mQPS// = 90.
 * a. Find //x//.**

//mQPR// + //mRPS// = //mQPS// Angle Addition Theorem 70 - 4//x// + 18//x// - 8 = 90 Substitution 62 + 14//x// = 90 Simplify. 14//x// = 28 Subtract 62 from each side. //x// = 2 Divide each side by 14.

Since a rectangle is a parallelogram, opposite sides are parallel. S, alternate interior angles are congruent.
 * b. Find //y//.**

//PQS// //QSR// Alternate Interior Angles Theorem //mPQS// = //mQSR// Definition of congruent angles 7//y// + 6 = //y//2 - 2 Substitution 0 = //y//2 - 7//y// - 8 Subtract 7//y// and 6 from each side. 0 = (//y// -8)(//y// + 1) Factor.

//y// - 8 = 0 //y// + 1 = 0 //y// = 8 //y// = -1 Disregard //y// = -1 because it yields angle measures less than 0.