Geometry Quest Exam Worksheet
GEOMETRY
QUEST
3rd Quarter Final Examination
Student:
Date:
Score: / 50
Instructions:
Select the best answer for each of the 50 multiple-choice questions. Ensure you show work for calculation-based problems on a separate sheet if needed. Diagrams are not necessarily drawn to scale.
Part I: Polygons & Quadrilaterals
1.What is the sum of the interior angle measures of a convex pentagon?
A 180°
B 360°
C 540°
D 720°
2.In a convex octagon, three of the exterior angles each have a measure of \(x^\circ\). The other five exterior angles each have a measure of \((2x+7)^\circ\). Find the value of \(x\).
A 25
B 35
C 45
D 50
3.Which property is TRUE for all parallelograms?
A Diagonals are congruent.
B Opposite angles are supplementary.
C Diagonals bisect each other.
D All four sides are congruent.
4.Find the value of \(x\) in the parallelogram shown. (Note: \(6\) and \(x\) are opposite sides).
A 3
B 6
C 9
D 12
6 x
5.In parallelogram \(ABCD\), \(m\angle A = 101^\circ\). What is \(m\angle B\)?
A 79°
B 101°
C 180°
D 90°
6.Which of the following must be a rhombus?
A A quadrilateral with four right angles.
B A parallelogram with congruent diagonals.
C A parallelogram where diagonals are perpendicular.
D A trapezoid with congruent legs.
7.Quadrilateral \(PQRS\) has vertices \(P(5, 1), Q(9, 6), R(5, 11),\) and \(S(1, 6)\). What is the most specific name for this quadrilateral?
A Rectangle
B Rhombus
C Square
D Kite
8.The Pentagon building in Washington, D.C. is shaped like a regular pentagon. What is the measure of each interior angle?
A 72°
B 90°
C 108°
D 120°
9.Find the length of the middle shelf (\(x\)) in the plant stand shown. The shelves are equally spaced circular sections.
A 9 in.
B 10.5 in.
C 12 in.
D 21 in.
6 in. x in. 15 in.
10.In a kite, one angle measures \(90^\circ\) and another non-congruent angle measures \(30^\circ\). What is the measure of the largest angle in the kite?
A 120°
B 135°
C 150°
D 210°
11.A rectangle must be a square if:
A Its diagonals bisect each other.
B Two adjacent sides are congruent.
C Its opposite sides are congruent.
D It has four right angles.
12.Find the sum of the measures of the exterior angles of a convex 20-gon.
A 360°
B 1800°
C 3240°
D 3600°
13.In parallelogram \(JKLM\), diagonals \(\overline{JL}\) and \(\overline{KM}\) intersect at point \(E\). If \(JE = 3.5\) and \(ME = 6\), what is the length of diagonal \(\overline{KM}\)?
A 7
B 9.5
C 12
D 18
14.Which quadrilateral always has diagonals that are perpendicular?
A Rectangle
B Isosceles Trap.
C Rhombus
D Parallelogram
15.If a trapezoid has one pair of congruent base angles, it must be:
A A right trapezoid.
B A parallelogram.
C An isosceles trapezoid.
D A kite.
16.The measure of an interior angle of a regular polygon is \(144^\circ\). How many sides does the polygon have?
A 8
B 10
C 12
D 15
17.In quadrilateral \(ABCD\), \(\overline{AB} \parallel \overline{CD}\) and \(m\angle A = 70^\circ\). What measure of \(\angle D\) would make \(ABCD\) an isosceles trapezoid?
A 70°
B 110°
C 180°
D 90°
18.Three vertices of parallelogram \(JKLM\) are \(J(-2, -1), K(0, 2),\) and \(L(4, 3)\). Find the coordinates of vertex \(M\).
A (2, 0)
B (6, 6)
C (2, -2)
D (3, 4)
19.Which statement is always true for a rectangle?
A The diagonals are perpendicular.
B The diagonals are congruent.
C Each diagonal bisects a pair of opposite angles.
D All four sides are congruent.
20.In parallelogram \(ABCD\), \(m\angle A = 2x+5\) and \(m\angle C = 3x-20\). Find the value of \(x\).
A 15
B 25
C 35
D 45
Part II: Similarity & Proportion
21.Two polygons are similar if and only if their corresponding angles are ______ and their corresponding side lengths are ______.
A Congruent; Proportional
B Proportional; Congruent
C Congruent; Congruent
D Supplementary; Proportional
22.Find the scale factor of quadrilateral \(ABCD\) to \(EFGH\). (Sides: \(CD=12, BC=8, GH=9, FG=?\))
A 2 : 3
B 3 : 2
C 3 : 4
D 4 : 3
12 8
ABCD
9 x
EFGH
23.If quadrilateral \(ABCD \sim EFGH\) and the scale factor of \(ABCD\) to \(EFGH\) is \(2 : 3\), what is the ratio of their perimeters?
A 2 : 3
B 4 : 9
C 8 : 27
D 1 : 1
24.Two similar triangles have a scale factor of \(3 : 5\). If the area of the smaller triangle is \(18\) square units, what is the area of the larger triangle?
A 30 units²
B 50 units²
C 60 units²
D 100 units²
25.Which similarity theorem requires knowing that two angles of one triangle are congruent to two angles of another?
A SSS Similarity
B SAS Similarity
C AA Similarity
D ASA Similarity
26.A 6-foot tall person casts a 4-foot shadow. At the same time, a nearby flagpole casts a 20-foot shadow. How tall is the flagpole?
A 13.3 feet
B 24 feet
C 30 feet
D 120 feet
27.Triangle \(LMN\) has sides 6, 8, and 10. Triangle \(PQR\) has sides 9, 12, and 15. Which statement is true?
A The triangles are similar by AA.
B The triangles are similar by SAS.
C The triangles are similar by SSS.
D The triangles are not similar.
28.To prove two triangles are similar by SAS, you must show that one angle of one triangle is congruent to one angle of the other, and ______.
A all sides are congruent.
B the sides including the angles are proportional.
C the other two angles are congruent.
D the hypotenuses are proportional.
29.If \(\triangle ABC \sim \triangle DEF\) and the ratio of their corresponding sides is \(1 : k\), what is the ratio of their areas?
A 1 : k
B 1 : 2k
C 1 : k²
D 1 : √k
30.If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides ______.
A Equally
B Perpendicularly
C Proportionally
D Asymmetrically
31.Find the value of \(x\) given that the internal segment is parallel to the base.
A 8
B 12
C 16
D 48
8 4 24 x
32.The Converse of the Triangle Proportionality Theorem is used to prove that two lines are ______.
A Perpendicular
B Parallel
C Intersecting
D Skew
33.If three parallel lines intersect two transversals, then they divide the transversals proportionally. This is known as the ______ Theorem.
A Triangle Proportionality
B Three Parallel Lines
C Transversal Proportionality
D Both B and C are commonly used names.
34.In the diagram, \(\vec{AD}\) bisects \(\angle CAB\). Find the value of \(x\).
A 2.67
B 9.375
C 12.0
D 24.0
A C B D 8 15 5 x
35.In a perspective drawing, two lines that are parallel in real life are drawn such that they meet at a ______.
A Starting point
B Center point
C Vanishing point
D Focal point
36.If \(\triangle PQR \sim \triangle XYZ\) with a scale factor of \(5 : 2\), and the perimeter of \(\triangle PQR\) is \(100\) cm, what is the perimeter of \(\triangle XYZ\)?
A 40 cm
B 250 cm
C 16 cm
D 20 cm
37.To estimate building height, a mirror is placed \(100\) ft from the base. A student stands \(4\) ft from the mirror. If the student's eyes are \(5.6\) ft high, what is the building's height?
A 71.4 ft
B 140 ft
C 160 ft
D 224 ft
38.If the scale factor of two similar solids is \(a : b\), what is the ratio of their surface areas?
A a : b
B a² : b²
C a³ : b³
D √a : √b
39.Which of the following is NOT a valid way to prove two triangles are similar?
A AA
B SSS
C SSA
D SAS
40.If two triangles are similar, then the ratio of any two corresponding altitudes is ______ the scale factor.
A Equal to
B Square of
C Half of
D Square root of
41.A scale model of a park has length \(2\) ft and width \(1.4\) ft. If the actual park is \(800\) yd long, what is the width of the actual park?
A 400 yards
B 560 yards
C 1120 yards
D 1600 yards
42.In \(\triangle ABC \sim \triangle DEF\), \(AB = 6\), \(BC = 9\), and \(AC = 12\). If \(DE = 10\), what is the length of \(\overline{EF}\)?
A 15
B 18
C 20
D 22.5
43.Which theorem justifies that \(\frac{AD}{DB} = \frac{AE}{EC}\) in a triangle where \(\overline{DE} \parallel \overline{BC}\)?
A SAS Similarity Theorem
B Triangle Proportionality Theorem
C Pythagorean Theorem
D AA Similarity Theorem
44.Three parallel lines intersect transversals. Segments on one are \(7\) and \(4\). On the other, segments are \(x\) and \(6\). Find \(x\).
A 3.5
B 10.5
C 12
D 42
45.Two triangles are similar with scale factor \(k\). The area of the larger is \(A\). What is the area of the smaller?
A A · k²
B A / k²
C A / k
D A · √k
46.If \(\triangle ABC \sim \triangle DEF\), and \(m\angle A = 40^\circ, m\angle B = 60^\circ\), what is the measure of \(\angle F\)?
A 40°
B 60°
C 80°
D 100°
47.Two right triangles are always similar if:
A They both have a 90° angle.
B One acute angle of one is congruent to one acute angle of the other.
C The hypotenuses are congruent.
D The legs are proportional to the hypotenuse.
48.In \(\triangle ABC\), segment \(\overline{DE}\) is parallel to \(\overline{BC}\). If \(AD=4, DB=6,\) and \(AE=8\), find the length of \(\overline{EC}\).
A 10
B 12
C 14
D 16
49.Rectangles A and B are similar. A has dimensions \(4 \times 6\). B has dimensions \(10 \times 15\). What is the scale factor of A to B?
A 1 : 2
B 2 : 5
C 3 : 5
D 4 : 10
50.If two polygons are similar, their corresponding sides are ______.
A Congruent
B Parallel
C Proportional
D Perpendicular
End of Examination • Geometric Mastery Series
