8-3+Study+Guide


 * Lesson 8-3**


 * Example 1 Write a Proof**


 * Write a paragraph proof for Theorem 8.10.**
 * Given:** //P// //R//, //Q// //S//
 * Prove:** //PQRS// is a parallelogram

Because two points determine a line, we can draw. We now have two triangles. We know the sum of the angle measures of a triangle is 180, so the sum of the angle measures of two triangles is 360. Therefore, //mP// + //mQ// + //mR// + //mS// = 360.
 * Paragraph Proof:**

Since //P// //R// and //Q// //S//, //mP// = //mR// and //mQ// = //mS//. Substitute to find that //mP// + //mP// + //mQ// + //mQ// = 360, or 2(//mP//) + 2(//mQ//) = 360. Dividing each side of the equation by 2 yields //mP// + //mQ// = 180. This means that consecutive angles are supplementary and.

Likewise, 2//mP// + 2//mS// = 360, or //mP// + //mS// = 180. These consecutive supplementary angles verify that. Opposite sides are parallel, so //ABCD// is a parallelogram.

**CONSTRUCTION** **Wood lattice panels are**
 * Example 2 Properties of Parallelograms**

The overlapping boards form a parallelogram when each pair of opposite segments is congruent. If the person making the panels measures each pair of opposite segments, and they are the same, then the boards form parallelograms.
 * usually made in a configuration of parallelograms.**
 * Explain how the person who made the panels could**
 * verify that the overlapped boards form**
 * parallelograms.**