4) Given: Lines m and n are perpendicular to line l.
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1 Geometry Benchmark 2 Please choose the best answer choice for each of the following questions. 1) Which of the following is not an example of deductive reasoning? A Everyone Rickey knows owns a cell phone. Therefore, everyone owns a cell phone. B Mammals are warm blooded. Dogs are mammals. Therefore, dogs are warm blooded. C Fish breathe through their gills. Sharks are fish. Therefore, sharks breathe through gills. D Every U.S Senator must be a citizen of the United States. Barbara Boxer is a U.S. Senator. Therefore, Barbara Boxer is a citizen of the United States. Standard: G 1.0 3) Which of the following is not sufficient to prove that a quadrilateral is a parallelogram? A Showing that both pairs of opposite sides are congruent. B Showing that both pairs of opposite angles are congruent. C Showing that the diagonals bisect each other. D Showing that the sum of the measures of the interior angles is 360. Standard: G 2.0 4) Given: Lines m and n are perpendicular to line l. l 2) Which of the following best describes inductive reasoning? A Accepting the meaning of a term without a definition. B Using logic to draw conclusions based on accepted statements. C Inferring a general truth by examining a number of specific examples. D Defining mathematical terms to correspond with physical objects. Standard: G 1.0 m n Which is the first step in a proof that lines m and n are parallel? A Assuming line m is not parallel to line n. B Assuming line m is parallel to line n. C Assuming line m is perpendicular to line l. D Assuming line m is not perpendicular to line l. Standard: G 2.0 Geometry Benchmark 1 Page 1
2 5) Which of the following cannot be used as a reason in a proof? A Definition B Property C Postulate D Conjecture Standard: G 2.0 6) Given: ABCD is a parallelogram with diagonals!" and!". Which of the following must be true? A!"!" B!"!" C!"!" D!" bisects!" Standard: G 3.0 7) If the conclusion is false in a valid argument, then which of the following must be false? A Inverse B Converse C Argument D Hypothesis 8) Which of the following can serve as a counterexample to the assertion that alternate interior angles are never supplementary? A A line that is parallel to two parallel lines B A transversal that forms a 45 angle with two parallel lines C A transversal that is perpendicular to two parallel lines D A transversal that froms a 180 angle with two parallel lines Standard: G 3.0 9) Given:!"!", and!"!". A B X C W Which is enough to prove that the triangles are congruent? A!"!" B!"!" C CAB WXY D ABC YWX Standard: G 4.0 Y Standard: G 3.0 Geometry Benchmark 1 Page 2
3 10) 13) Two triangles are congruent if each side of one triangle is congruent to which of the following of the second triangle? A Base B Corresponding angle C Corresponding side D Triangles cannot be congruent Standard: G ) In rectangle RECT, diagonals RC and ET intersect at point X. Which of the following statements need not be true? A!"!" B!" is perpendicular!" C!"!" D!"!" Correct B Standard: G ) Given:!" and!" intersect at B,!"!", and 1! 2. 14) What is the largest possible whole number base of an isosceles triangle with equal sides each of 7.3 inches? A 7 in. B 10 in. C 14 in. D 15 in. Standard: G ) Maurice is hiking through a forest. He wants to make a triangular fire pit. He has a 3-foot branch and an 8-foot branch. He finds four more branches with lengths listed below. Which will allow him to complete his triangular fire pit? Which can be used to prove! ABD! CBE? A ASA B HL C SAS D SSS A 2 ft. branch B 4 ft. branch C 7 ft. branch D 12 ft. branch Standard: G 6.0 Standard: G 5.0 Geometry Benchmark 1 Page 3
4 16) Which of the following can be drawn without any congruent sides? 18) In the parallelogram ABCD, which two angles are congruent? A Rhombus B Parallelogram C Kite D Trapezoid Standard: G ) In the figure below, lines a and b are parallel and are cut by transversal c. a 1 c A!"# and!"# B!"# and!"# C!"# and!"# D!"# and!"# Standard: G 7.0 b 2 19) In the figure below,!"!". What is the value of x? What is the sum of angles 1 and 2? A 90 B 180 C 360 D Cannot be determined Correct B Standard: G 7.0 A 60 B 65 C 85 D 90 Standard: G 12.0 Geometry Benchmark 1 Page 4
5 20) Two exterior angles of a triangle measure 153 and 105. Which could not be an interior angle measure of the triangle? 23) Gregory plans to use a straightedge and compass to construct a perpendicular bisector of!" in ABC shown below. A 27 B 75 C 78 D 102 Standard: G ) What is the value of x? Which shows the construction? A 61 B 92 C 119 D 149 Standard: G ) Rocio is using a straightedge and a compass to do the construction shown below. Which best describes Rocio s construction? A A line through P parallel to!" B A line through P intersecting!" C Angle bisector of!" D Angle bisector of Q. Standard: G 16.0 Standard: G 16.0 Geometry Benchmark 1 Page 5
6 24) Brittany is constructing a line parallel to line l through point P. Which of the following should be her first step? 26) If TRI were plotted on a coordinate grid, which statement would prove that TRI is a right triangle? A The slope!" times the slope of!" is -1. B The slope of!" times the slope of!" is 1. C The slope of!" equals the slope of!". D The slope of!" is greater than that of!". Standard: G ) What type of figure is formed by the points F(-2,1), G(0,5), H(6,5), and J(4,1)? A Square B Rectangle C Trapezoid D Parallelogram Standard: G 17.0 Standard: G ) A parallelogram is formed by the point A(-4,6), B(2,6), C(4,3), and D(-2,3). What is the length of diagonal!"? A 3 B 5 C 7 D 10 Correct B Standard: G ) A sewing club is making a quilt consisting of 25 squares with each side of the square measuring 30 centimeters. If the quilt has 5 rows and five columns, what is the perimeter of the quilt? A 150 cm B 300 cm C 600 cm D 900 cm Standard: G 8.0 Geometry Benchmark 1 Page 6
7 29) A rectangle has an area 24 cm 2 and length 3 cm. What is its perimeter? 31) Figure ABCD is a rhombus. Find its area. A 72 cm B 22 cm C 11 cm D 8 cm Correct B Standard: G ) Find the area of trapezoid ABCD? A 12 square inches B 20 square inches C 24 square inches D 60 square inches Standard: G 10.0 A 24 sq in. B 28.5 sq in. C sq in. D 40.5 sq in. Standard: G ) If the base of parallelogram MNOP is 1 inch less than twice its height, which expression represents the area of the parallelogram? A (!)(2! 1) B 2(2! 1) C (2! 1)!! D!!!!!! Standard: G 10.0 Geometry Benchmark 1 Page 7
8 33) The right triangle shown on the coordinate plane below has vertices at (-3,5), (-8,-4) and (5,5). What is its area, in square units? 35) What is!!? A 24 B 36 C 32 D 72 A 30 B 66 C 84 D 96 Standard: G 13.0 Standard: G ) What is the!!"#? A 45 B 61 C 82 D 119 Correct B Standard: G 13.0 Geometry Benchmark 1 Page 8
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