Review Questions for Unit Exam 32 Geometry 1.Intheaccompanyingdiagramof parallelogramabcd,diagonals AC and BD intersectate,ae&=3x& 4,andEC&=x&+12. Whatisthevalueofx? (1)8 (3)20 (2)16 (4)40 2.Intheaccompanyingdiagramof parallelogramabcd,diagonals AC and BD 2 intersectate, BE = x, and ED = x 10. 3 Whatisthevalueofx? (1)F30(3)F6 (2)30(4)6 3.Intheaccompanyingdiagramof parallelogramabcd,m A&=(2x&+10)and m B&=&3x.Findthenumberofdegreesin m B.
4. In the accompanying diagram of parallelogram ABCD, m B = 5 x, and m C = 2x + 12. Find the number of degrees in D. 5.Themeasuresoftwoconsecutiveanglesof aparallelogramareintheratio5:4.whatis themeasureofanobtuseangleofthe parallelogram? (1)20 (3)100 (2)80 (4)160 6.InrhombusABCD,themeasure,ininches, of AB is 3x + 2 and BC is x + 12.Findthe numberofinchesinthelengthof DC. 7. In rectangle ABCD, AC = 3x+15 and BD = 4x 5. Find the length of AC.
8.Asshownintheaccompanyingdiagram, arectangulargatehastwodiagonal supports.if m 1= 42,whatis m 2? 9. In the accompanying diagram of rectangle ABCD, m BAC = 3x + 4 and m ACD = x + 28. What is m CAD? (1) 12 (3) 40 (2) 37 (4) 50 10. Which statement is false? (1)All parallelograms are quadrilaterals. (2)All rectangles are parallelograms. (3)All squares are rhombuses. (4) All rectangles are squares. 11.Whichstatementisnot$alwaystrue aboutaparallelogram? (1)Thediagonalsarecongruent. (2)Theoppositesidesarecongruent. (3)Theoppositeanglesarecongruent. (4)Theoppositesidesareparallel.
12. Which quadrilateral must have diagonals that are congruent and perpendicular? (1) rhombus (3) trapezoid (2) square (4) parallelogram 13. A quadrilateral whose diagonals bisect each other and are perpendicular is a (1) rhombus (3) trapezoid (2) rectangle (4) parallelogram 14.Inacertainquadrilateral,two oppositesidesareparallel,andtheother twooppositesidesarenotcongruent. Thisquadrilateralcouldbea (1)rhombus (3)square (2)parallelogram (4)trapezoid 15. The cross section of an attic is in the shape of an isosceles trapezoid, as shown in the accompanying figure. If the height of the attic is 9 feet, BC = 12 feet, and AD = 28 feet, find the length of AB to the nearest foot.
16. In the diagram below of isosceles trapezoid DEFG, DE GF, DE = 4x 2, EF = 3x + 2, FG = 5x 3, and GD = 2x + 5. Find the value of x. 17.IsoscelestrapezoidABCDhas diagonals AC and BD.If AC = 5x + 13 and BD = 11x 5, whatisthevalueof x? (1)28 (3)3 (2)10 3 4 (4) 1 2 18. In the diagram of trapezoid ABCD below, diagonals AC and BD intersect at E and ΔABC ΔDCB. Which statement is true based on the given information? (1) AC BC (3) CDE BAD (2) CD AD (4) CDB BAC
19. Given: A(-2,2), B(6,5), C(4,0), D(-4,-3) Prove: ABCD is a parallelogram but not a rectangle. [The use of the grid is optional.] 20. The coordinates of quadrilateral ABCD are A(-1,-5), B(8,2), C(11,13), and D(2,6). Using coordinate geometry, prove that quadrilateral ABCD is a rhombus. [The use of the grid is optional.]
21. 080134b, P.I. G.G.69 Given: A(1,6), B(7,9), C(13,6), and D(3,1) Prove: ABCD is a trapezoid. [The use of the grid is optional.] 22. Given: T(-l,l), R(3,4), A(7,2), and P(-l,-4) Prove: TRAP is a trapezoid. TRAP is not an isosceles trapezoid. [The use of the grid is optional.]