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

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

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

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

Lesson 6-4: Rhombus & 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. 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

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