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Published byJulius Maxwell Modified over 9 years ago
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6.4 Rhombuses, Rectangles, and Squares Day 4
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Review Find the value of the variables. 52° 68° h p (2p-14)° 50° 52° + 68° + h = 180° 120° + h = 180 ° h = 60° p + 50° + (2p – 14)° = 180° p + 2p + 50° - 14° = 180° 3p + 36° = 180° 3p = 144 ° p = 48 °
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Special Parallelograms Rhombus A rhombus is a parallelogram with four congruent sides.
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Special Parallelograms Rectangle A rectangle is a parallelogram with four right angles.
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Special Parallelogram Square A square is a parallelogram with four congruent sides and four right angles.
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Corollaries RRhombus corollary AA quadrilateral is a rhombus if and only if it has four congruent sides. RRectangle corollary AA quadrilateral is a rectangle if and only if it has four right angles. SSquare corollary AA quadrilateral is a square if and only if it is a rhombus and a rectangle.
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Example PQRS is a rhombus. What is the value of b? P Q R S 2b + 3 5b – 6 2b + 3 = 5b – 6 9 = 3b 3 = b
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Review In rectangle ABCD, if AB = 7f – 3 and CD = 4f + 9, then f = ___ A) 1 B) 2 C) 3 D) 4 E) 5 7f – 3 = 4f + 9 3f – 3 = 9 3f = 12 f = 4
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Example PQRS is a rhombus. What is the value of b? P Q R S 3b + 12 5b – 6 3b + 12 = 5b – 6 18 = 2b 9 = b
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Theorems for rhombus A parallelogram is a rhombus if and only if its diagonals are perpendicular. A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. L
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Theorem of rectangle A parallelogram is a rectangle if and only if its diagonals are congruent. A B CD
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Match the properties of a quadrilateral 1. The diagonals are congruent 2. Both pairs of opposite sides are congruent 3. Both pairs of opposite sides are parallel 4. All angles are congruent 5. All sides are congruent 6. Diagonals bisect the angles A. Parallelogram B. Rectangle C. Rhombus D. Square B,D A,B,C,D B,D C,D C
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