Geometry EOC Review Problems Student Name __________________

Module A: Basic Tools of Geometry

MA.912.G.1.1 Distance Formula Review Problems

1. What is the distance between Point A (3,-2) and Point B (6, 2)?

2. What is the distance between Point (-4,-4) and Point (2,-7)?

3. What is the distance between Point F (2, 4) and Point G (5, 0)?

4. What is the distance between Point (0, 3) and Point (-5, -1)?

5. An airplane flies on a map from Point A (-2,8) to Point Z (-5,-3). What is the length of the journey made by the airplane?

6. Jack’s house is located in Central Park at Point (3, 7). Jill lives up the hill at Point (-6, 4). Jill wants to walk to Jack’s house. What is the length of the walk she must take to get to Jack’s house?

7. A circle centered at the origin contains Point (-5,-6) on its perimeter. What is the length of the radius of the circle?

8. A circle centered at Point (3, 1) contains Point (-1, 6) on its perimeter. What is the length of the radius of the circle?

MA.912.G.1.1 Midpoint Formula & Missing Endpoint Review Problems

9. What is the midpoint for Point D (5, 3) and Point E (6, 2)?

10. What is x-coordinate for the midpoint for Point (-5, -6) and Point (-3, -8)?

11. What is y- coordinate for the midpoint for Point J (-1, 0) and Point K (-7, 4)?

12. Jack’s house is located in Central Park at Point (3, 7). Jill lives up the hill at Point (-6, 4). She calls Jack and asks him to meet her halfway at a coffee shop. What will be the coordinates of the coffee shop?

13. A road runs from Point (7, 2) to Point (2, 7). The city wants to install a traffic light at the halfway point to better control traffic. What is the y-coordinate of the traffic light?

14. A train starts its journey at Point A (4, 7) and ends at Point B (-2, 1). At what point will the train have reached the halfway point of its journey?

15. Segment PQ contains midpoint T. If segment PT = (6x-3) and QT = (2x + 5), what is the length of PQ?

16. A line segment contains Point X (-2, 3) and midpoint (1, 0). What is the y-coordinate of the missing endpoint?

17. A line segment contains Point T (0, -4) and midpoint (-1, 3). What is the x-coordinate of the missing endpoint?

18. A train travels from Point A to Point B. If Point A is (4,2) and the half way point of the journey is (1,-2), what are the coordinates for Point B?

19. A student D.C. tour starts at the Washington Monument located at Point (-8, 1). They stop for lunch at the halfway point of their tour at Point (0, -4). What are the coordinates for the other endpoint of their tour?

MA.912.G.5.1 Pythagorean Theorem Review Word Problems20. A ladder leaning up against a house is 15’ long. If the bottom of the ladder is placed 9’ from the

house, how high up on the house will the ladder reach?

21. A kitten is stuck in a tree 12’ off the ground. The base of a ladder is placed 6’ from the tree. How long must the ladder be in order to reach the kitten?

22. A tree is 46’ high and at 3pm in the afternoon on December 22, it casts a shadow that is 67’ long. What is the distance in feet from the top of the tree to the end of the shadow?

23. A flag pole has a support wire that is 119’ long. The wire is fixed to a point in the ground that is 45’ from the base of the flag pole. How tall is the flag pole?

24. A helicopter flies 34 miles to reach a client. It then flies 21 miles to drop that client off at their destination. Based on the drawing below, how long is the helicopter’s return flight?

25. The bottom end of a ramp at a warehouse is 10 feet from the base of the main dock and is 11 feet long. How high is the dock?

26. An airplane lands at an airport 60 miles east and 25 miles north of where it took off. How far apart are the two airports?

Module B/C: Logic & Parallel & Perpendicular Lines

1. Read the statement shown below.“If two supplementary angles are congruent, then they are right angles.”Which of these is the contrapositive of the statement?

A. If two supplementary angles are right angles, then they are congruent.B. If two supplementary angles are congruent, then they must be right angles.C. If two supplementary angles are not right angles, then they are not congruent.D. If two supplementary angles are not congruent, then they are not right angles.

2. Which of these is a valid conclusion?

A. All sergeants clear a fitness test.Harry has cleared a fitness test.Therefore, Harry is a sergeant.

B. All sergeants clear a fitness test.Harry has not cleared a fitness test.Therefore, Harry is not a sergeant.

C. All sergeants clear a fitness test.Harry is a sergeant.Therefore, Harry has not cleared a fitness test.

D. All sergeants clear a fitness test.Harry is not a sergeant.Therefore, Harry has not cleared a fitness test.

3. Read the statement shown below.

“All squares are parallelograms.”Which of the following is a sufficient condition for the above statement to be true?

A. A square has equal diagonals.B. A square has four right angles.C. A square has its opposite sides parallel.D. A square has diagonals which intersect at right angles.

4. Jason has listed the following conditions for Quadrilateral DEFG to be a kite.

1. DEFG is definitely a kite if the diagonals are perpendicular.2. DEFG is definitely a kite if angle EFH is equal to GFH.3. DEFG is definitely a kite if DE ≅ DG.4. DEFG is definitely a kite if FE ≅ FG.5. DEFG is definitely a kite if the longer diagonal bisects the shorter one.6. DEFG is definitely a kite if angle DEF is equal to DGF.7. DEFG is definitely a kite if DE is not congruent to FE.

Which conditions can be used together justify that DEFG is a kite?A. Conditions 1, 3, and 6B. Conditions 5 and 6C. Conditions 1 and 6D. Conditions 3, 4, and 7

5. Write the contrapositive of the following statement.“If Grandma comes to visit then we always have a pot of coffee ready.A. If there is no coffee prepared then Grandma is not visiting.B. If there is coffee prepared then Granma is visiting.C. If Grandma is not visiting then there is no coffee prepared.D. If Grandma is not visiting then we always have coffee ready.

6. Which of the following is the contrapositive of the following statement?"If it rains, then the ground will be wet."A. If the ground is not wet, then it did not rain.B. If the ground is wet, then it rained.C. If it does not rain, then the ground will not be wet.D. If the ground is not wet, then it rained.

7. In the figure below, p is parallel to q. Which of the following are corresponding angles?

A. ∠ 1 and ∠ 2 B. ∠ 1 and ∠ 3 C. ∠ 2 and ∠ 3 D. ∠ 3 and ∠ 4

8. In the diagram, GH IJ.

If m ∠ GLK = 55 and m ∠ EFJ = 120, what is m ∠ KEF?A. 55 B. 60 C. 65 D. 70

9. Which best describes the relationship between lines m and n?

A. They are transversal.B. They are skew.C. They are perpendicular.D. They are parallel.

Angle Proof

10. Choose the correct reason for Statement #2.A. Complementary Angles B. Supplementary Angles C. Corresponding Angles D. Vertical Angles

11. Choose the correct reason for Statement #3.A. Vertical Angles B. Complementary Angles C. Right Angles D. Alternate Interior Angles

12. Choose the correct reason for Statement #5.A. Addition Property B. SubstitutionC. Symmetrical Property of Congruence D. Right Angles

13. In the diagram below, line d cuts three lines to form the angles shown.

If any, which lines are parallel?A. a ∥ b B. b ∥ c C. a ∥ c D. No parallel lines

14. Given m ∥ n, m ∠ 2 = 10x − 15 ° and m ∠ 4 = 15x.

What is m ∠ 5?A. 45 ° B. 63 ° C. 117 ° D. 135 °

15. Boone Park Tennis Complex is located between two parallel streets, Park Street and Herschel Street. The tennis complex faces Park Street and is bordered by two brick walls that intersect Herschel Street at point C, as shown below.

What is the measure, in degrees, of ∠ BCA, the angle formed by the park's two brick walls?A. 38 ° B. 42 ° C. 67 ° D. 71 °

Algebraic ProofGiven: m ∠ 1 = 4x + 9, m ∠ 2 = 7(x + 4)Find: m ∠ 3

Proof:

16. Which of the following is the correct reason for statement three in the proof above?

A. Same-Side Interior Angles TheoremB. Corresponding Angles PostulateC. Triangle Inequality TheoremD. Straight Line Postulate

17. Which of the following is the correct reason for statement seven in the proof above?

A. Addition Property of EqualityB. Subtraction Property of EqualityC. Multiplication Property of EqualityD. Division Property of Equality

18. Which of the following is the correct reason for statement eleven in the proof above?

A. Same-Side Interior Angles TheoremB. Corresponding Angles PostulateC. Triangle Inequality TheoremD. Straight Line Postulate

Module D: Triangles

MA912.G.2.2

MA.912.G 2.2

MA.912.G 2.2

MA.912.G.4.7

MA.912.G.4.6

MA.912.G.4.2

MA.912.G.4.8

Module E: Quadrilaterals

What is the correct reason for Statement #4?A. Alternate Interior Angles B. Vertical Angles C. Property of Triangles D. Substitution

What is the correct reason for Statement #5?A. SSS B. SSA C. ASA D. AAS

What is the correct reason for Reason #6?

Module F: Transformation and SimilarityDetermine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.1. 2.

3. The polygons are similar. Find the value of x.

4. Myra is playing a board game. After 12 turns, Myra has landed on a blue space 3 times. If the game will last for 100 turns, predict how many times Myra will land on a blue space.

5. Find the length of line segment PR. 6. Isosceles trapezoid ABCD is located at Point A (0,0) Point B (8,0) Point C (6,4) and Point D (2,4). Similar

trapezoid WXYZ has Point W (-1,1) and Point X (-1,5).

What are the coordinates for Point Y and Point Z?

Determine whether the dilation from A to B is an enlargement or a reduction. Then find the scale factor of the dilation.

7. 8.

9. Parallelogram JKLM has vertices J(2, 1), K(7, 1), L(6, –3), and M(1, –3). What is the coordinates of the image of K if the parallelogram is rotated 270° about the origin?

Determine whether BC ∥DE. Justify your answer.

10.

11.

12.

13. On a map, Wilmington Street, Beech Drive, and Ash Grove Lane appear to all be parallel. The distance from Wilmington to Ash Grove along Kendall is 820 feet and along Magnolia, 660 feet. If the distance between Beech and Ash Grove along Magnolia is 280 feet, what is the distance between the two streets along Kendall?

14. A local furniture store sells two versions of the same chair: one for adults, and one for children. Find the value of x such that the chairs are similar.

Module G: Special Right Triangles and TrigonometryEasy Special Right Review Problems

Easy Trig Review Problems

60°20cm

8√2in

8cm

10m

54’

?

60°

60°

10m

Moderate to Hard Special Right & Trig Problems

A 40-foot-long escalator rises from the first floor to the second floor of a shopping mall. The escalator makes a 30° angle with the horizontal. How high above the first floor is the second floor?

A 54’ flag pole casts a shadow a noon. What is the approximate length of the shadow in feet?

Find the area & perimeter of the rectangle.

Find area & perimeter of the square.

Find the area of the rhombus.

Find the perimeter of the rectangle (regular hexagon). What is the shaded area?

289161

240

4900’x

29°

451’

x

36°

A hiker dropped his backpack over one side of a canyon onto a ledge below. The angle of depression to the backpack is 32°. If the width of the canyon is 115 feet, how far down did the backpack fall?

What decimal represents… A) sin G B) cos G C) tan G

The angle of elevation to an airplane viewed by a person at an airport is 29°. The pilot reports that the altitude is 4900 feet. How far away from the person is the airplane?

Sailors on a ship at sea spot the light from a lighthouse. The angle of elevation to the light is 25°. The light of the lighthouse is 30 meters above sea level. How far from the shore is the ship?

A support wire needs to be added to a cell phone tower for stability. The wire is mounted to the ground 451’ from the tower. How long must the wire be to reach the top of a tower using an angle of elevation of 36°?

11

14

F

36°

80ft

20mm

10 in

16m

Find the measure of angle F.

Find the perimeter of the rectangle.

Find the area of this regular polygon.

Find the area of this regular polygon.

Find the area of this regular polygon.

Module H: Area & Volume

1. The height of a parallelogram is 10 feet more than its base. If the area of the parallelogram is 1200 square feet, find its base and height.

2. The base of a triangle is one half of its height. If the area of the triangle is 196 square millimeters, find its base and height.

Find the perimeter and area of each parallelogram. Round to the nearest tenth if necessary.

3. 4.

5. One diagonal of a kite is twice as long as the other diagonal. If the area of the kite is 400 square meters, what are the lengths of the diagonals?

6. A trapezoid has a height of 40 inches, a base of 15 inches, and an area of 2400 square inches. What is the length of the other base?

Find the area of each trapezoid, rhombus, or kite.

7. 8.

9. The area of a circle is 201.1 square inches. Find the radius.

10. Sadie wants to draw a clock face on a circular piece of cardboard. If the clock face has a diameter of 20 centimeters and is divided into congruent pieces so that each sector is 30°, what is the area of each piece?

Find the area of each figure. Round to the nearest tenth if necessary.

11. 12.

For each pair of similar figures, use the given areas to find the scale factor from the unshaded to the shaded figure. Then find x.

13. 14.

Find the lateral area and surface area of each object. Round to the nearest tenth if necessary.

15. 16.

17. Mr. Beattie built a conical storage shed. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed?

18. The start of the pyramid age began with King Zoser’s pyramid, erected in the 27th century B.C. In its original state, it stood 62 meters high with a rectangular base that measured 140 meters by 118 meters. Find the volume of the original pyramid.