Properties of Parallelograms

Properties of Parallelograms Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are Supplementary. Diagonals bisect each other. 2 IF ABCD is a parallelogram, find each missing measure. B 15 m X33 10 m 38/57 m 8 437 8.4m A 43 23 64 23 C D a) AB = 8.4m e) aligned m angle BAD = 6 zeta^ m angle ADC= underline underline ||^ 4 |^ * aligned d) b) AC = 20m c) RE = 7vm f) m angle ABD = 114 deg If PQRS is a parallelogram. Find the measure of PSR (7x - 13) deg (4x - 5) deg R 7v - 13 +7x|-13 4x - 5 + 4x - 1 22x - 34 = 360 angle PSQ = 7(18) * 0.13 = 7x + 4x - 180 + 5 + 13 S 7x - 13 + 4x - 5 = 180 11x = 193.5 (11x)/11 = 198/(1 ^ 4) = x = 18 [[394], [2], [16]] P 1 113 Gina Wiban (All Things Algebra), 2014 PARALLELOGRAMS Gina Wilson (All Things Algebra), 2014 RECTANGLES RHOMBI SQUARES Properties of Rectangles • Opposite sides are parallel • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are 190° • Diagonals bisect each other. Rectangles have the same properties as parallelograms, plus • All right angles. • Diagonals are congruent 4 IF JKLM is a rectangle, Find each missing measure. K L If PQRS is a rectangle, find the measure of ZOPT (10x + 1)' T R 61 20 m N 35 m S 19 m M 59 (16x - 17) deg 9t - 31 = 59 16x - 17 = 10x + 7 15x - 10x = 1 + 17 (4x)/h - 18 6 x = 31 16(3) - 17 = 37 deg 10(3) + 1 = 31 deg a) KL = 35m d) m angle KLM = underline odot(0^ ) QPT-59 b) NL = 20m e) m angle LMK = 6 deg c) KM = 40m m angle LJM = underline 19^ 2 * Gina Wilson (All Things Algetiro), 2014 RECTANGLES RHOMBI SQUARES TRAPEZOIDS Properties of Rhombi • Opposite sides are parallel • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are 180° • Diagonals bisect each other. + Rhombi have the same properties as parallelograms, plus: • All sides are congruent • Diagonals are right angles. • Diagonals bisect opposite angles IF WXYZ is a rhombus, find each missing measure X 27 IF EFGH is a rhombus, Find the measure of ZFGE. (5y - 7) deg G (8x - 49) deg 145 W 15 21 in/30 Y 27 27 ^ 9 + b ^ 2 \approx 21 ^ 2 b ^ 2 = boxed 288 729 + b ^ 2 = 441 b = 16.97 H 8x - 19 = 5x - 7 3x - 49 = - 7 3x = 42 x = 14 MeFGE 270 Gina Wilson (All Things Algebra). 2014 27 in 51 boxed 31 * 21 6 x + 51 + x + 39 = matrix angle1\\ 180 matrix (2x)/2 = 90/2 * x = 45 d) mZXZW = 45 a) XY = 21 e) m angle XWZ = 10 deg b) WP = 27 c) PZ = 16.017 f) m angle 2YW = 3 * (0) deg RHOMBI SQUARES TRAPEZOIDS Properties of Squares Opposite sides are parallel • Opposite sides are congruent • Opposite angles are congruent • Consecutive angles are. 180° • Diagonals bisect each other. • All right angles. • All sides are Congruent. • Diagonals are congruent Diagonals are perpendicular • Diagonals biset opposite angles. Squares have ALL the properties of parallelograms, rectangles, and rhombl. If BCDE is a square, Aind each missing measure C D 8 ft 1 8 B E 0) CE16 8822 b) BC=13 8-113 T c) m∠CFD=90 d) m∠DBE IF QRST is a square, find GS R S U 21 cm 01:29.7cmm