Geometry Quest Exam Worksheet Condensed
Geometry Quest
3rd Quarter Examination
Name:
Date:
Score: / 50
Part I: Polygons & Quadrilaterals
1. Sum of interior angle measures of a convex pentagon?
A) 180° B) 360° C) 540° D) 720°
2. Octagon: 3 ext \(\angle\)s = \(x^\circ\), 5 = \((2x+7)^\circ\). Find \(x\).
A) 25 B) 35 C) 45 D) 50
3. Which is TRUE for all parallelograms?
A) Diagonals are congruent
B) Diagonals bisect each other
C) Opposite \(\angle\)s are supplementary
4. Find \(x\) in the \(\square\) shown (Opposite sides: 6, \(x\)).
A) 3 B) 6 C) 9 D) 12
5. In \(\square ABCD\), \(m\angle A = 101^\circ\). Find \(m\angle B\).
A) 79° B) 101° C) 180° D) 90°
6. Which of the following must be a rhombus?
A) Diagonals are \(\perp\)
B) Four right angles
C) \(\cong\) diagonals
7. Vertices \(P(5,1), Q(9,6), R(5,11), S(1,6)\). Name:
A) Rect. B) Rhombus C) Square D) Kite
8. Regular pentagon: each interior angle?
A) 72° B) 108° C) 120° D) 144°
9. Plant stand: shelves are 6, \(x\), 15. Find \(x\).
A) 9 B) 10.5 C) 12 D) 21
10. Kite: angles are \(90^\circ, 30^\circ\). Largest angle?
A) 120° B) 135° C) 150° D) 210°
11. A rectangle must be a square if:
A) Adjacent sides \(\cong\)
B) Diagonals bisect
12. Sum of exterior angles of convex 20-gon?
A) 360° B) 1800° C) 3240° D) 3600°
13. \(\square JKLM, JE=3.5, ME=6\). Find diagonal \(KM\).
A) 7 B) 12 C) 9.5 D) 18
14. Which always has perpendicular diagonals?
A) Rectangle B) Rhombus C) Trapezoid D) \(\square\)
15. Trapezoid with \(\cong\) base \(\angle\)s is:
A) Isosceles B) Right
16. Regular polygon int \(\angle = 144^\circ\). Sides?
A) 8 B) 10 C) 12 D) 15
17. \(ABCD, AB \parallel CD, m\angle A=70^\circ\). Isosceles if \(\angle D\):
A) 70° B) 110°
18. \(J(-2,-1), K(0,2), L(4,3)\). Find vertex \(M\).
A) (2,0) B) (6,6) C) (2,-2) D) (3,4)
19. Which statement is always true for a rectangle?
A) Diagonals \(\cong\)
B) Diagonals \(\perp\)
C) Sides \(\cong\)
20. \(\square ABCD, m\angle A=2x+5, m\angle C=3x-20\). Value of \(x\)?
A) 15 B) 25 C) 35 D) 45
Part II: Similarity & Proportion
21. Polygons similar if \(\angle\)s ___ and sides ___.
A) \(\cong\); Proportional
B) Proportional; \(\cong\)
22. Scale factor of \(ABCD\) to \(EFGH\) (12 to 9)?
A) 2:3 B) 4:3 C) 3:4 D) 3:2
23. If scale factor is 2:3, ratio of perimeters?
A) 2:3 B) 4:9 C) 8:27 D) 1:1
24. Similar \(\triangle\)s, SF 3:5. Small area 18. Larger?
A) 30 B) 50 C) 60 D) 100
25. Similarity theorem: two angles \(\cong\)?
A) SSS B) SAS C) AA D) ASA
26. 6-ft tall person, 4-ft shadow. Flagpole, 20-ft shadow?
A) 13.3 B) 24 C) 30 D) 120
27. \(\triangle\)s with sides 6,8,10 and 9,12,15 are similar by:
A) AA B) SAS C) SSS D) Not
28. Proving similar by SAS: show one \(\angle \cong\) and:
A) Inc. sides proportional
B) Inc. sides \(\cong\)
29. Corr. side ratio is 1:k. Ratio of areas?
A) 1:k B) 1:2k C) 1:k² D) 1:√k
30. Parallel line to one side divides other sides ___.
A) Equally B) Proportionally
31. Find \(x\) given segments parallel to base (8,4,24,\(x\)).
A) 8 B) 12 C) 16 D) 48
32. Converse of Triangle Prop Thm proves lines:
A) Parallel B) Skew
33. 3 parallel lines divide transversals ___.
A) Proportionally B) Equally
34. \(\vec{AD}\) bisects \(\angle CAB\). (Sides 8, 15; Base 5, \(x\)). Find \(x\).
A) 2.67 B) 9.375
35. Perspective: parallel lines meet at a ___ pt.
A) Center B) Vanishing C) Focal D) Start
36. SF 5:2, large perimeter 100. Small perimeter?
A) 40 cm B) 250 cm C) 20 cm D) 16 cm
37. Mirror 100ft from base, eyes 5.6ft, student 4ft. Height?
A) 71.4 B) 140 C) 160 D) 224
38. Scale factor of solids is a:b. Surface area ratio?
A) a:b B) a²:b² C) a³:b³ D) \(\sqrt{}\)
39. Which is NOT valid to prove similarity?
A) AA B) SSA C) SAS D) SSS
40. Ratio of corr. altitudes is ___ the SF.
A) Equal to B) Square of
41. Model \(2 \times 1.4\). Actual 800 yd long. Actual width?
A) 560 B) 1120 C) 400 D) 1600
42. \(\triangle ABC \sim \triangle DEF\), 6,9,12 and 10,EF,15. Find EF.
A) 15 B) 18 C) 20 D) 22.5
43. Thm for \(\frac{AD}{DB} = \frac{AE}{EC}\) with \(\overline{DE} \parallel \overline{BC}\)?
A) Triangle Prop.
B) SAS Sim.
44. 3 parallel lines: segments 7, 4 and \(x\), 6. Find \(x\).
A) 10.5 B) 3.5 C) 12 D) 42
45. SF \(k\), larger area \(A\). Smaller area is:
A) \(A / k^2\) B) \(A \cdot k^2\)
46. Corr. \(\triangle\), \(\angle\)s \(40^\circ, 60^\circ\). Measure of 3rd \(\angle\)?
A) 80° B) 100°
47. Right triangles are always similar if:
A) One acute \(\angle \cong\) to another
48. Parallel segment divides sides 4, 6 and 8, \(x\). Find \(x\).
A) 12 B) 10 C) 16 D) 5.3
49. Rects \(4 \times 6\) and \(10 \times 15\). Scale factor?
A) 2:5 B) 3:5
50. If polygons are similar, corr. sides are ___.
A) Proportional B) \(\cong\)
End of Examination • Geometric Mastery Series
