Lecture 6 4 Rhombi and Squares Lesson 6

Lecture 6 -4 Rhombi and Squares Lesson 6 -4: Rhombus & Square 1

Rhombus Definition: A rhombus is a parallelogram with four congruent sides. ≡ ≡ Since a rhombus is a parallelogram the following are true: l Opposite sides are parallel. l Opposite sides are congruent. l Opposite angles are congruent. l Consecutive angles are supplementary. l Diagonals bisect each other Lesson 6 -4: Rhombus & Square 2

Properties of a Rhombus Theorem: The diagonals of a rhombus are perpendicular. Theorem: Each diagonal of a rhombus bisects a pair of opposite angles. Lesson 6 -4: Rhombus & Square 3

Rhombus Examples. . . Given: ABCD is a rhombus. Complete the following. 1. 9 units If AB = 9, then AD = ______. 2. 65° If m<1 = 65, the m<2 = _____. 3. 90° m<3 = ______. 4. 100° If m<ADC = 80, the m<DAB = ______. 5. 10 If m<1 = 3 x -7 and m<2 = 2 x +3, then x = _____. Lesson 6 -4: Rhombus & Square 4

Square Definition: A square is a parallelogram with four congruent angles and four congruent sides. Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals. l l l l Opposite sides are parallel. Four right angles. Four congruent sides. Consecutive angles are supplementary. Diagonals are congruent. Diagonals bisect each other. Diagonals are perpendicular. Each diagonal bisects a pair of opposite angles. Lesson 6 -4: Rhombus & Square 5

Squares – Examples…. . . Given: ABCD is a square. Complete the following. 1. units and DC = _____. 10 units If AB = 10, then AD = 10 _____ 2. 5 units If CE = 5, then DE = _____. 3. 90° m<ABC = _____. 45° m<ACD = _____. 5. 90° m<AED = _____. Lesson 6 -4: Rhombus & Square 6