Download Part I: 10 Open-Ended Questions

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CP Geometry
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FINAL EXAM REVIEW
Part I: 10 Open-Ended Questions
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 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 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.
(a)
����;
� ∥ 𝐺𝐾
Given: 𝐿𝐽
M is the midpoint of ����
𝐿𝐺
Prove: Δ𝐿𝐽𝑀 ≅ Δ𝐺𝐾𝑀
(b)
Given: ����
𝐿𝑁 bisects ∠𝑂𝐿𝑀 and ∠𝑂𝑁𝑀
�����
Prove: ����
𝑂𝑁 ≅ 𝑀𝑁
3.
4.
5.
Area of Triangles, Rectangles and Trapezoids [10-2]
(a)
(b) Find the area of an isosceles
trapezoid with base angles 60° and
bases 18 cm and 40 cm.
Area of Regular Polygons [10-3]
(a)
Find the area of a square with apothem 4√2.
(b)
Find the area of a regular hexagon with radius 12.
Perpendicular Bisectors [3-8]
���� has endpoints A(-3, -2) and B(3, 4). Write the equation of the line that contains the
(a)
𝐴𝐵
����.
perpendicular bisector of 𝐴𝐵
(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 𝑀𝑁
6.
Proving a Parallelogram [6-7]
Graph each quadrilateral on graph paper. Then determine the most precise name for each.
Explain your answer.
(a)
(b)
7.
A(3, 5), B(7, 6), C(6, 2), D(2, 1)
J(2, 1), K(5, 4), L(8, 1), M(2, -3)
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?
8.
9.
10.
Area of a Sector and Segment [10-7]
(a)
(b)
Properties of Parallelograms [6-2 and 6-3]
What values of x and y make the quadrilateral a parallelogram?
(a)
PT = 2x, TR = y + 4, QT = x + 2, TS = y
(b)
QP = x + 2, RS = y, QR = 2x, PS = y + 3
Tangent Lines [12-1]
Find x.
(a)
(b)
Part II: 30 Multiple Choice Questions
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 𝑦1 +𝑦2
,
2
2
�
Distance Formula: �(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2
Properties of Parallelograms
Surface Area of Prism: 𝑆𝐴 = 𝐿𝐴 + 2𝐵
Tangents of a Circle
Equation of a Circle: (𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2
Transformations: Translations, Reflections and Rotations
Inscribed Angles
Pythagorean Theorem
Angles Formed by Parallel Lines
4
Volume of a Sphere: 𝑉 = 𝜋𝑟 2
3
Midsegment of a Triangle
Constructions – Identify an Angle Bisector (Incenter), Perpendicular Bisector (Circumcenter),
Medians (Centroid) and Altitude (Orthocenter)
Multiple Choice Review.
Circle the correct answer(s).
There may be more than one correct answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Answer each problem.
14.
Find the values of x and w to the nearest tenth.
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.
23.
25.
27.
24.
26.
28.