8-2+Study+Guide


 * Lesson 8-2**

Write a two-column proof of Theorem 8.4.
 * Example 1 Proof of Theorem 8.4**
 * Given:** //WXYZ//

//X// //Z//
 * Prove:** //W// //Y//

//X// and //Y// are supplementary //Y// and //Z// are supplementary || //X// //Z// ||
 * Proof:**
 * Statements**
 * Reasons** ||
 * 1.** //WXYZ// ||
 * 1.** Given ||
 * 2.**, ||
 * 2.** Definition of parallelogram ||
 * 3.** //W// and //X// are supplementary
 * 2.**, ||
 * 2.** Definition of parallelogram ||
 * 3.** //W// and //X// are supplementary
 * 3.** //W// and //X// are supplementary
 * 3.** If parallel lines are cut by a transversal, consecutive interior angles are supplementary. ||
 * 4.** //W// //Y//
 * 4.** //W// //Y//
 * 4.** Supplements of the same angles are congruent. ||

**ALGEBRA** **Quadrilateral //PQRS// is a parallelogram.**
 * Example 2 Properties of Parallelograms**

//mQRS// = 18 + 31 or 49 Angle Addition Theorem
 * Find //mQPS//, //mPSR//, and //n//.**

//QPS// //QRS// Opp. s of are. //mQPS// = //mQRS// Definition of congruent angles //mQPS// = 49 Substitution

//mQPS// + //mPSR// = 180 Cons. s of are suppl. 49 + //mPSR// = 180 Substitution //mPSR// = 131 Subtract 49 from each side.

Opp. sides of are. //PS// = //QR// Definition of congruent segments 36 = 4//n// Substitution 9 = //n// Divide each side by 4.