8-5+Study+Guide


 * Lesson 8-5**


 * Example 1 Proof of Theorem 8.15**
 * Given:** //ABCD// is a rhombus.


 * Prove:**

By the definition of a rhombus,. A rhombus is a parallelogram and the diagonals of a parallelogram bisect each other, so bisects at //X//. Thus,. because congruence of segments is reflexive. Thus, //ABX// //CBX// by SSS. //BXA// //BXC// by CPCTC. //BXA// and //BXC// also form a linear pair. Two congruent angles that form a linear pair are right angles. //BXA// is a right angle, so  by the definition of perpendicular lines.
 * Proof:**

**ALGEBRA** **Use rhombus //BCDE// and the given**
 * Example 2 Measures of a Rhombus**

//m//3 = 90 The diagonals of a rhombus are perpendicular. //y//2 + 26 = 90 Substitution //y//2 = 64 Subtract 26 from each side. //y// = 8 Take the square root of each side. The value of //y// can be 8 or -8.
 * information to find the value of each variable.**
 * a. If //m//3 = //y//2 + 26, find //y//.**

//mBCD// = //mBED// Opposite angles are congruent. //mBCD// = 38 The diagonals of a rhombus bisect the angles. So, //mCED// = (38) or 19.
 * b. Find //mCED// if //mBCD// = 38.**

**COORDINATE GEOMETRY** **Determine whether**
 * Example 3 Squares**

**Explore** Plot the vertices on a coordinate plane.
 * parallelogram //WXYZ// is a //rhombus//, a //rectangle//, or**
 * a //square//. List all that apply. Explain**

**Plan** If the diagonals are perpendicular, then //WXYZ// is either a rhombus or a square. The diagonals of a rectangle are congruent. If the diagonals are congruent and perpendicular, then //WXYZ// is a square.

**Solve** Use the Distance Formula to compare the lengths of the diagonals.