Geometry — Benchmark 1 Page 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.

Correct A Standard: G 1.0

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.

Correct C 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°.

Correct D Standard: G 2.0

4) Given: Lines m and n are perpendicular to

line l .

l

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 .

Correct A Standard: G 2.0

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5) Which of the following cannot be used as a

reason in a proof? A Definition

B Property

C Postulate

D Conjecture Correct D 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 !"

Correct D 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

Correct D Standard: G 3.0

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

Correct C Standard: G 3.0

9) Given: !" ≅ !", and !" ≅ !".

A B X

C W Y Which is enough to prove that the triangles are congruent?

A !" ≅ !"

B !" ≅ !"

C ∠CAB ≅ ∠WXY

D ∠ABC ≅ ∠YWX Correct A Standard: G 4.0

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11) 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 4.0

12) Given: !" and !" intersect at B, !" ≅ !", and ∠1!≅ ∠2. Which can be used to prove!△ABD!≅ △CBE? A ASA

B HL

C SAS

D SSS Correct A Standard: G 5.0

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 Correct C Standard: G 5.0

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. Correct C Standard: G 6.0

15) 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? A 2 ft. branch

B 4 ft. branch

C 7 ft. branch

D 12 ft. branch Correct C Standard: G 6.0

10)

Geometry — Benchmark 1 Page 4

16) Which of the following can be drawn without any congruent sides?

A Rhombus

B Parallelogram

C Kite

D Trapezoid Correct D Standard: G 7.0

17) In the figure below, lines a and b are parallel and are cut by transversal c.

c a 1 b 2

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

18) In the parallelogram ABCD, which two angles are congruent?

A ∠!"# and ∠!"#

B ∠!"# and ∠!"#

C ∠!"# and ∠!"#

D ∠!"# and ∠!"# Correct C Standard: G 7.0

19) In the figure below, !" ∥ !". What is the value of x?

A 60

B 65

C 85

D 90 Correct C Standard: G 12.0

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20) Two exterior angles of a triangle measure 153° and 105°. Which could not be an interior angle measure of the triangle? A 27° B 75° C 78° D 102° Correct D Standard: G 12.0

21) What is the value of x?

A 61

B 92

C 119

D 149 Correct C Standard: G 12.0

22) 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. Correct D Standard: G 16.0

23) Gregory plans to use a straightedge and compass to construct a perpendicular bisector of !" in △ABC shown below.

Which shows the construction?

Correct A Standard: G 16.0

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24) Brittany is constructing a line parallel to line l through point P. Which of the following should be her first step?

Correct C Standard: G 16.0

25) 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 17.0

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 !". Correct A Standard: G 17.0

27) 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 Correct D Standard: G 17.0

28) 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

Correct C Standard: G 8.0

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29) A rectangle has an area 24 cm2 and length 3 cm. What is its perimeter?

A 72 cm

B 22 cm

C 11 cm

D 8 cm Correct B Standard: G 8.0

30) Find the area of trapezoid ABCD?

A 24 sq in.

B 28.5 sq in.

C 29.25 sq in.

D 40.5 sq in. Correct C Standard: G 8.0

31) Figure ABCD is a rhombus. Find its area.

A 12 square inches

B 20 square inches

C 24 square inches

D 60 square inches Correct C Standard: G 10.0

32) 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 ! !!!!!

Correct A Standard: G 10.0

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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?

A 24

B 36

C 32

D 72

Correct C Standard: G 10.0

34) What is the !∠!"#?

A 45° B 61° C 82° D 119° Correct B Standard: G 13.0

35) What is !∠!?

A 30° B 66° C 84° D 96° Correct C Standard: G 13.0