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Name _________________________________________________________________ Date _____________________Honors Geometry FINAL EXAM REVIEW
1. Angle of Elevation and Depression
(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
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: Open-Ended Questions
3. Area of Triangles, Rectangles and Trapezoids
(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
(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
(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
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
(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
(a) (b)
9. Properties of Parallelograms
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
Find x.
(a) (b)
11. Parallel Lines
In the picture to the right, lines l and m are parallel. The m∠PAX = 31, and the m∠PBY = 54. What is the m∠APB?
12. Law of Sines and Cosines
(a) The Bermuda Triangle is a historically famous region of the Atlantic Ocean. The vertices of the triangle are formed by Miami, FL; Bermuda; and San Juan, Puerto Rico. The approximate dimensions of the Bermuda Triangle are shown in the figure below. What is the distance from Bermuda to Miami to the nearest mile?
(b) After fielding a ground ball, a picture is located 110 feet from first base and 57 feet from home plate as shown in the figure below. To the nearest tenth, what is the measure of the angle with its vertex at the pitcher?
13. Geometric Probability
Find the probability that a random point lies in the shaded region.
(a) (b)
14. Circles
(a) (b)
Part II: 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 r2
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.
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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. 24.
25. 26.
27. 28.
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