EOC Geometry Practice Test 10th Grade

1) You are trying to prove that quadrilateral 𝐸𝐹𝐺𝐻 is a square. You have already proven that all four sides are congruent.

Which statement, if true, would prove that 𝐸𝐹𝐺𝐻 is a square?

2) The cardboard box below is used by a company to package new laptops. If the company plans to increase the length of the box by 2 inches, what is the minimum amount of extra cardboard needed to construct the new box?

3) A company is planning to sell juice in boxes represented by the figure shown below. What is the total surface area of the box?

4) Cylinders A and B have the same height. The radius of cylinder A is twice the radius of cylinder B.

How does the volume of cylinder A compare to the volume of cylinder B?

5) Mari created the circular window represented below. She knew that ∠1 and ∠2 were supplementary and that ∠1 ≅ ∠3 because they were vertical angles. What must be true about ∠2 and ∠3?

6) The diameter of a cone is 16 meters. If the height is 1.5 times its radius, which value is closest to the volume of the cone?

7) How much paper is needed to cover a rectangular bulletin board that is 29 in. wide and 37 in. high?

8) John measured the sides of four triangles. He measured the side lengths of one triangle incorrectly. Which triangle was measured incorrectly?

9) Mikayla is filling a glass sphere with water. If the diameter of the sphere is 12 inches, what is the minimum amount of water she needs to completely fill the sphere?

10) Joe’s garden is the shape of a hexagon. The measures of 5 of the angles are: 160°, 90°, 60°, 160°, and 80°. What is the measure of the remaining angle?

11) Which theorem can be used to show that the two triangles below are congruent?

12) A circular sidewalk is being constructed around the perimeter of a local park. A brick pathway will be added through the diameter of the circle as shown on the coordinate plane below, and a tree will be planted in the sidewalk at the center of the circle. What is the x-coordinate where the tree will planted?

13) A square base pyramid is shown below. Find its surface area.

14) Shawn has a greenhouse in the shape shown in the figure below. He keeps new plants in the room represented by the shaded area. What is the perimeter of the room that is shaded?

15) What is the measure of ∠𝐸 in the parallelogram below?

16) The surface area of the sphere below is 4𝜋². If the radius were to be divided by 2, how would the surface area be affected?

17) Kelvin is at his house located at (3, 4) on a coordinate plane and walks to the store located at (1, 0). The store is located exactly half way between Kelvin’s house and Mitch’s house. To the nearest tenth, what is the distance between Kelvin’s house and Mitch’s house?

18) The captain of a submarine views an iceberg from his periscope, as shown in the figure below.

What is the height of the iceberg to the nearest meter?

19) Frances bought a new refrigerator to replace her old refrigerator shown above. Her new refrigerator has the same length and width as the old refrigerator, but is 8 inches higher. How many more cubic inches of space are in Frances’s new refrigerator compared to her old refrigerator?

20) Figure 𝐴𝐵𝐶𝐷 below is a quadrilateral. What is the value of 𝑥?

21) The volume of Prism A is 1,536 m³ and the volume of Prism B is 375 m³ . What is the ratio of their surface area?

22) For ∆𝑋𝑌𝑍, \overline{\rm QR} ∥ \overline{\rm XZ}

What is the length of \overline{\rm RY}

23) Below is a drawing of Jeff’s yard. There is a circular fish pond near one corner. The diameter of the pond is 12 ft. How many square feet of grass are necessary to cover everything except the pond in Jeff’s yard?

24) A meter stick is held perpendicular to the ground. It forms a shadow that is 1.8 𝑚 long. At the same time, a flagpole forms a shadow that is 7.2 𝑚 long. How tall is the flagpole?

25) The radius of a cylinder is multipled by 6 while the height is kept the same. What effect does this have on the volume of the cylinder?

The volume will be multipled by –

26) A rope is tied to the bottom of a hot air balloon as shown below. The rope makes an angle of 35° with the ground and is 75 𝑓𝑡. long. How far is the bottom of the balloon from the ground to the nearest foot?

27) The perimeter of the square below is 36. What is the length of the diagonal, 𝑥?

28) A cereal box is 10.4 inches high, 7.4 inches long, and 2.3 inches wide. What is the volume of the cereal box rounded to the nearest cubic inch?

29) An engineer designed a steel beam, shown below. The horizontal parts that form the top and bottom are parallel. To build the cross pieces, the engineer needs to know the measure of the angles shown. The measure of ∠1 = 110 degrees and 𝑚∠2 = 105 degrees. What are the measures of ∠3 and ∠4?

30) Which is closest to the area of the shaded sector of circle C?

31) A cat is stuck in a tree. A firefighter’s 15-foot ladder is leaning against the tree. The ladder and the ground form a 62° angle. How high above the ground does the ladder touch the tree?

32) Two parallel lines, 𝑚 and 𝑛, are cut by a transversal, 𝑡, as shown in the figure below.

If 𝑚∠2 = 2𝑥 + 7 and 𝑚∠7 = 3𝑥 − 13, what is the measure of ∠7?

33) Polygon 𝑆𝑇𝑈𝑉𝑊 is shown below

After the polygon 𝑆𝑇𝑈𝑉𝑊 is reflected across the y-axis, what are the coordinates of 𝑆′, the image of point 𝑆 after the transformation?

34) In the figure below, lines k, m, and n are parallel.

What is the sum of 𝑚∠1 and 𝑚∠2?

35) What is the converse of this statement?
𝐼𝑓 𝑎 𝑟𝑜𝑎𝑑 𝑠𝑖𝑔𝑛 𝑖𝑠 𝑟𝑒𝑑, 𝑡ℎ𝑒𝑛 𝑖𝑡 𝑖𝑠 𝑎 𝑠𝑡𝑜𝑝 𝑠𝑖𝑔𝑛.

36) What regular polygon has an exterior angle that measures 60 degrees?

37) Jeff lives on Oak Street, and Tom lives on Main Street.

How much farther, to the nearest yard, is it for Tom to walk down Main Street and turn on Oak Street to get to Jeff’s house than if he travels the shortest distance between the houses through an empty field?

38) Which 3-dimensional shape can be formed from the net below?

39) The diameter of a tractor tire is 5 feet. Rounded to the nearest hundredth, how far will the tractor move when the wheel rotates once?

40) A solid-glass sphere is cast with a radius of 30 𝑐𝑚. What is the volume, to the nearest whole number, of this sphere?