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GEOMETRY 4-#13 Review – Quadratics Name: ___________________ Period: _____ To complete each definition, find the appropriate word in the second column. a. b. c. d. e. f. g. h. i. parallelogram trapezoid square base angles isosceles trapezoid rectangle consecutive angles kite rhombus 1. A(n) ________ is a parallelogram with four right angles. 2. A(n) _________ is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. 3. Angles of a polygon that share a common side are _______. 4. A(n) ________ is a quadrilateral with exactly one pair of parallel sides. 5. A(n) _______ is a parallelogram with four congruent sides. 6. A(n) ________ is a quadrilateral with both pairs of opposite sides parallel. 7. A(n) ________ is a parallelogram with four congruent sides and four right angles 8. A(n) ________ is a trapezoid whose nonparallel sides are congruent. 9. Two angles that share a base of a trapezoid are its _________. Find the measures of the numbered angles for each parallelogram. 3 10. 3 11. 2 38° 12. 3 2 63° 79° 1 2 37° 1 99° Find the values for the variables for which ABCD must be a parallelogram. 13. A 14. A (3y – 20)° (4y+4)° B B O C (2x+6)° (4x)° D D 15. C For the trapezoids and kites, find the measures of angles 1 and 2. a) 2 77° b) 1 54° 82° 2 1 c) d) 62° 2 22° 2 1 112° 1 AO 3 y 3 BO 4x 2 CO 3x DO 3 y 1 16. In rhombus ABCD, AB = 6, AC = 8, and mABC 30. a) mADC _______ b) mAEB ______ c) BC = _____ d) AE = ______ e) mBAD ______ f) mCDE ______ 17. Given: Prove: 18. A E D C R parallelogram SPQR and S SQ bisects PQR SQ bisects PSR P Q Complete the following proof by filling in the blanks Q R T S Given: QRST is a rectangle Prove: QS RT Statements Reasons 1. QRST is a rectangle 2. QT RS 3. QTS and RST are right angles 4. QTS RST 5. TS TS 6. ____ ____ 7. QS RT Factor the following: 19. x 2 3 x 28 20. x 2 13 x 42 21. 2 x 2 x 36 22. 3 x 2 13x 10 B 23. Solve for x and y: 3x 4 y 9 x 2 y 7 2 x 3 y 2 24. 5 x 3 y 26 25. Find the area of the triangle: 2.5cm 4cm 2cm 5cm 26. Find the area of the parallelogram: 27. Find the area of the trapezoid: 28. If the perimeter of the rectangle is 126m, what is the area? 29. Find the area of the kite. 30. In the trapezoid below, what is the length of the short base: 31. The area of the trapezoid is 273 in2. What is the length of c? 32. Find the area of the shaded portion of the trapezoid: For the Quadrilaterals test you may use 1 pg handwritten notes (front and back) and your beige sheet. I suggest that you use either the “Quadrilaterals Resource Page” notes that we did in class or the Quadrilaterals “tree,” but you could also make your own page. You may also use a calculator. ANSWERS: 1. F 2. H 3. G 4. B 5. I 6. A 7. C 8. E 9. D 10. Angle 1=angle 3 =101, angle 2 = 19, angle 3 = 101 11. Angle 2 = angle 3= 26 13. x=29, y = 28 12. Angle 1 = 38, angle 2 = 43, angle 3 = 99 14. x = 4, y = 5 15. A. Angle 1 = 103, angle 2 = 77 b. angle 1 = angle 2 = 22 angle 2 = 118 c. angle 1 = 68, angle 2 = 90 d. angle 1 = 68, 16. A 30 b. 90 c. 6 d. 4 e. 150 f. 15 parallelogram SPQR and 17. SQ bisects PQR given, use opposite sides of a parallelogram are congruent by def’n of a parallelogram and that SQ is congruent to itself by the reflexive prop of congruence. Then triangle PSQ is congruent to triangle RQS by SSS. Then angle PSQ is congruent to angle RQS by CPCTC. Angle PQS is congruent to angle RQS by definition of angle bisector. Angle RSQ is congruent to angle PSQ by transitive property of congruence and SQ bisects angle PQR by definition of angle bisector. 18. given, opp sides of a rectangle are congruent, def. of rectangle, all right angles are congruent, reflexive property of congruence, triangle QTS and triangle RST are congruent by SAS, CPCTC 19. (x+4)(x-7) 20 (x-7)(x-6) 24 (4, -2) 27. 216 m^2 25. 5 cm^2 28. 950 m^2 21. (2x-9)(x+4) 22. (3x-2)(x+5) 23. (5, 6) 26. 55 cm^2 29. 252 cm^2 30. 12 in 31. 27 in 32. 40 cm^2