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Name __________________________ Common Core Geometry R Date ______________ Hwk #28 Parallelograms 1. Check all properties that apply to each quadrilateral. Name Both pairs of opposite sides are parallel. Both pairs Both pairs of Diagonals of opposite opposite are equal. angles =. sides =. Diagonals bisect each other. Diagonals are perpendicular All angles to each equal. other. Diagonals bisect opposite angles. All sides equal. parallelogram rectangle rhombus square 2. Circle the letter of the correct multiple choice answer. a) Which statement is not always true about a parallelogram? (1) The diagonals are congruent. (3) The opposite angles are congruent. (2) The opposite sides are congruent. (4) The opposite sides are parallel. b) A parallelogram must be a rectangle if its diagonals (1) are congruent (2) bisect each other (3) are perpendicular to each other (4) bisect the angles whose vertices they connect. c) If the diagonals of a parallelogram are perpendicular and not congruent, then the parallelogram is (1) a rhombus (2) a square (3) a rectangle (4) a trapezoid d) Which statement is false? (1) All parallelograms are quadrilaterals. (2) All rectangles are parallelograms. (3) All squares are rhombuses. (4) All rectangles are squares. Draw a diagram and show all work. 3. In parallelogram STUV, SV = x + 3, VU = 2x - 1, and TU = 4x - 3. Find ST. 4. In rectangle ABCD, diagonals AC and BD are drawn. m≮BAC = 3x + 4 and m≮ACD = x + 28. Find m≮CAD. OVER 1 5. PQRS is a parallelogram. m≮SQP = 4x - 2, m≮QSR = 3x + 6, and m≮QPR = 8x - 4. Solve for x. What specials type of parallelogram is PQRS? Justify your answer. P Q S R 6. In rectangle ABCD, diagonals AC and BD intersect at E. If AC = 3x + 2, DE = x + 4, and AD = 2x. Find the length of CD. 7. The degree measures of two opposite angles of a parallelogram are represented by 3x + 40 and x + 70. Is the parallelogram a rectangle? Justify your answer. 8. QRST is a parallelogram. Find x, y, and z. Q R 330 5x T 9. Find x and y so that the quadrilateral is a parallelogram. 2y5 y+4 27 (3z)0 S 4x17 (3y+5)0 (5y13)0 2x1 2