part i: 10 open-ended questions
TRANSCRIPT
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 18°. Find
the distance from the base of the statue to the ship to the nearest thousandth of a foot.
(b) The world’s 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: 𝐿�̅� ∥ 𝐺𝐾̅̅ ̅̅ ; M is the midpoint of 𝐿𝐺̅̅̅̅
Prove: Δ𝐿𝐽𝑀 ≅ Δ𝐺𝐾𝑀
(b) Given: 𝐿𝑁̅̅ ̅̅ bisects ∠𝑂𝐿𝑀 and ∠𝑂𝑁𝑀
Prove: 𝑂𝑁̅̅ ̅̅ ≅ 𝑀𝑁̅̅ ̅̅ ̅
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 60° and bases 18 cm and 40 cm.
4. Area of Regular Polygons [10-3]
(a) Find the area of a square with apothem 4√2 cm.
(b) Find the area of a regular hexagon with radius 12 km.
5. Perpendicular Bisectors [3-8]
(a) 𝐴𝐵̅̅ ̅̅ has endpoints A(-3, -2) and B(3, 4). Write the equation of the line that contains the
perpendicular bisector of 𝐴𝐵̅̅ ̅̅ .
(b) Δ𝐿𝑀𝑁 has vertices L(3, 2), M(8, 6) and N(0,10). Find the equation of the line that
contains the perpendicular bisector of 𝑀𝑁̅̅ ̅̅ ̅.
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 Rollin’ 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) 𝑃𝑇 = 2𝑥, 𝑇𝑅 = 𝑦 + 4, 𝑄𝑇 = 𝑥 + 2, 𝑇𝑆 = 𝑦
(b) 𝑄𝑃 = 𝑥 + 2, 𝑅𝑆 = 𝑦, 𝑄𝑅 = 2𝑥, 𝑃𝑆 = 𝑦 + 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: (𝑛 − 2) ∙ 180
Area of a Square
Special Right Triangles: 30-60-90 and 45-45-90
Complementary Angles
Similar Right Triangles & Geometric Mean
Midpoint Formula: (𝑥1+𝑥2
2,
𝑦1+𝑦2
2 )
Distance Formula: √(𝑥1 − 𝑥2)2 + (𝑦1 − 𝑦2)2
Properties of Parallelograms
Surface Area of Prisms: 𝑆𝐴 = 𝐿𝐴 + 2𝐵
Tangents of a Circle
Transformations: Translations, Reflections and Rotations
Pythagorean Theorem
Angles Formed by Parallel Lines
Volume of a Sphere: 𝑉 =4
3𝜋𝑟3
Midsegment of a Triangle
Constructions – 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 C’
CP Geometry
7. 8.
10.
9.
11. 12.
13.
Answer each problem.
14. Find the values of x and w to the nearest tenth.
CP Geometry
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.
CP Geometry
23. 24.
25. 26.
27. 28.