CP Geometry
Name: ___________________________________________ Date: _____________________
CP Geometry FINAL EXAM REVIEW 2016
1. Angle of Elevation and Depression [8-4]
(a) A tourist looks out from the crown of the Statue of Liberty, approximately 250 feet above
ground. The tourist sees a ship in the harbor and measures the angle of depression as 18Β°. Find
the distance from the base of the statue to the ship to the nearest thousandth of a foot.
(b) The worldβs tallest unsupported flagpole is 282 feet tall steel pole in British Columbia. The
shortest shadow cast by the pole during the year is 137 feet long. To the nearest thousandth of
a degree, what is the angle of elevation of the sun?
2. Proving Congruent Triangles and Using CPCTC [4-4]
Write a formal two-column proof for each.
(a) Given: πΏοΏ½Μ οΏ½ β₯ πΊπΎΜ Μ Μ Μ ; M is the midpoint of πΏπΊΜ Μ Μ Μ
Prove: ΞπΏπ½π β ΞπΊπΎπ
(b) Given: πΏπΜ Μ Μ Μ bisects β ππΏπ and β πππ
Prove: ππΜ Μ Μ Μ β ππΜ Μ Μ Μ Μ
Part I: 10 Open-Ended Questions
CP Geometry
3. Area of Triangles, Rectangles and Trapezoids [10-2]
Find the area of each:
(a) (b) An isosceles trapezoid with base angles 60Β° and bases 18 cm and 40 cm.
4. Area of Regular Polygons [10-3]
(a) Find the area of a square with apothem 4β2 cm.
(b) Find the area of a regular hexagon with radius 12 km.
5. Perpendicular Bisectors [3-8]
(a) π΄π΅Μ Μ Μ Μ has endpoints A(-3, -2) and B(3, 4). Write the equation of the line that contains the
perpendicular bisector of π΄π΅Μ Μ Μ Μ .
(b) ΞπΏππ has vertices L(3, 2), M(8, 6) and N(0,10). Find the equation of the line that
contains the perpendicular bisector of ππΜ Μ Μ Μ Μ .
CP Geometry
6. Proving a Parallelogram [6-7]
Graph each quadrilateral on graph paper. Then determine the most precise name for each.
Explain your answer.
(a) A(3, 5), B(7, 6), C(6, 2), D(2, 1)
(b) J(2, 1), K(5, 4), L(8, 1), M(2, -3)
7. Construction of Perpendicular Bisectors & Circumcenters [5-2 & 5-3]
(a) A park director wants to build a T-shirt stand equidistant from the Rollinβ Coaster and the
Spaceship Shoot. Where should it be located? Construct the segment and explain your
answer.
(b) A town planner wants to locate a new fire station equidistant from the elementary, middle
and high schools. Where should he locate the station?
CP Geometry
8. Area of a Sector and Segment [10-7]
Find the area of the shaded region:
(a) (b)
9. Properties of Parallelograms [6-2 and 6-3]
What values of x and y make quadrilateral PQRS a parallelogram?
(a) ππ = 2π₯, ππ = π¦ + 4, ππ = π₯ + 2, ππ = π¦
(b) ππ = π₯ + 2, π π = π¦, ππ = 2π₯, ππ = π¦ + 3
10. Tangent Lines [12-1]
Find x.
(a) (b)
CP Geometry
Topics:
Bisectors [segment and angle]
Median, Altitude, Angle Bisector
Ways to Prove Triangles Congruent [SSS, SAS, ASA, AAS, HL]
Inequalities of Triangles
Isosceles Triangles
Triangle Inequality Theorem
Similar Triangles & Polygons
Sum of the Interior Angles of a Polygon: (π β 2) β 180
Area of a Square
Special Right Triangles: 30-60-90 and 45-45-90
Complementary Angles
Similar Right Triangles & Geometric Mean
Midpoint Formula: (π₯1+π₯2
2,
π¦1+π¦2
2 )
Distance Formula: β(π₯1 β π₯2)2 + (π¦1 β π¦2)2
Properties of Parallelograms
Surface Area of Prisms: ππ΄ = πΏπ΄ + 2π΅
Tangents of a Circle
Transformations: Translations, Reflections and Rotations
Pythagorean Theorem
Angles Formed by Parallel Lines
Volume of a Sphere: π =4
3ππ3
Midsegment of a Triangle
Constructions β Identify an Angle Bisector (Incenter), Perpendicular Bisector (Circumcenter),
Medians (Centroid) and Altitude (Orthocenter)
Part II: 30 Multiple Choice Questions
CP Geometry
Multiple Choice Review
Write/Circle the correct answer(s). *There may be more than one correct answer to some of these.
1. 2.
3. 4.
5. 6.
*Switch
D and Cβ
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7. 8.
10.
9.
11. 12.
13.
Answer each problem.
14. Find the values of x and w to the nearest tenth.
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15. 16.
17. Find the volume of the sphere.
18. Find the values of x and y that make ABCD a parallelogram.
19. Find the total surface area of the rectangular prism.
20.
21. 22.