Rhombi+and+Squares

Definitions Theorems 8.15, 8.16 and 8.17 Concept summary comparing squares and rhombi 3 sample problems

A rhombus is a quadrilateral with all four sides congruent. If a quadrilateral is both a rhombus and a rectangle, it is a square.

Theorem 8.15- The diagonals of a rhombus are perpendicular. Theorem 8.16- If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus (converse of 8.15) Theorem 8.17- Each diagonal of a rhombus bisects a pair of opposite angles

Concept Summary:

Rhombi: 1. A rhombus has all the properties of a parallelogram 2. All sides are congruent 3. Diagonals are perpendicular 4. Diagonals bisect the angles of the rhombus

Squares: 1. A square has all the properties of a parallelogram 2. A square has all the properties of a rectangle 3. A square has all the properties of a rhombus

Given: Triangle TPX is congruent to Triangle QPX is congruent to Triangle QRX is congruent to Triangle TRX. Prove: TPQR is a rhombus.