Name _________________________________________________________________ Date _____________________CP Geometry FINAL EXAM REVIEW

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) Given: LJ ∥GK ;M is the midpoint of LG

Prove: Δ LJM ≅ ΔGKM

(b) Given: ln bisects ∠OLM and ∠ONMProve: ON ≅ MN

Part I: 10 Open-Ended Questions

3. 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.

4. 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.

5. Perpendicular Bisectors [3-8]

(a) AB has endpoints A(-3, -2) and B(3, 4). Write the equation of the line that contains the 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) 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?

8. Area of a Sector and Segment [10-7]

(a) (b)

9. 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

10. 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+x22,y1+ y22 )

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=r2

Transformations: Translations, Reflections and Rotations

Inscribed Angles

Pythagorean Theorem

Angles Formed by Parallel Lines

Volume of a Sphere: V= 43π r3

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.

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7. 8.

9. 10.

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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.

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21. 22.

23. 24.

25. 26.

27. 28.