MIM-QC-Pythagorean Theorem (8th TEKS)

The side view of a ramp that Jessie built for his race cars is shown below. Find r, the length of the ramp to the nearest tenth is (a)   .

• A. 21 inches
• B. 15.7 inches
• C. 6.5 inches
• D. 17.4 inches

2. Three square rooms in Joey’s house meet to form a right triangle as shown. Joey is going to install new carpet to cover the floor of each room, as well as new trim around the edges of each room. Which is a true statement based on the diagram?

• F. The amount of carpet needed in Room Z should be the same as the carpet needed in both Room X and Room Y.
• G. The amount of trim needed in Room Z should be the same as the trim needed in both Room X and Room Y.
• H. Both statements above are true.
• J. Neither statements above are true.

3. Titus is building a triangular frame with three pieces of wood that measure 3 inches, 5 inches and 10 inches. Which of the following is true about the frame?

• A. The frame will be a right triangle because 5(2) + 3(2) < 10(2).
• B. The frame will be a right triangle because 5² + 3² < 10².
• C. The frame will not be a right triangle because 5² + 3² ≠ 10².
• D. The frame will not be a right triangle because 5(2) + 3(2) ≠ 10(2).

The side view of a wall shelf in Luke’s office is shown below. The diagonal support piece is 17 centimeters, and the piece against the wall is 8 centimeters. The approximate measure of w, the total width of the shelf, is (a)   .

• F. 8 centimeters
• G. 15 centimeters
• H. 22 centimeters
• J. 26 centimeters

5. The graph below shows the design for the front view of a doghouse that Jeremy plans to build. If each square on the graph represents 1 foot, find the perimeter of the design.

• A. 32 feet
• B. 26 feet
• C. 35 feet
• D. 28 feet

6. Kelsey’s school can be represented by Point A (9, 9). Point A can be translated 6 units left and 5 units down to create A’, the location of Kelsey’s house. Which of the following can be used to find the d, the diagonal distance between Point A and Point A’ on the grid?

• F. 6² + 5² = d²
• G. 9² + 4² = d²
• H. d² + 5² = 6²
• J. 6² – 5² = d²

The model below is used to show the relationship between the side lengths of a right triangle. The square that could be connected to side b of the triangle to correctly complete the model is (a)   .

• A. A square with side lengths of 40
• B. A square with side lengths of 10
• C. A square with side lengths of 50
• D. A square with side lengths of 20

8. Neil wants to join three pieces of metal to form a right triangle. Which of the following lengths could he use?

• F. 4, 4 and 8 feet
• G. 7.5, 10 and 12.5 feet
• H. 9, 11 and 23 feet
• J. 6, 12.5 and 96 feet

9. Find the total perimeter of the kite shown below. Round to the nearest tenth.

• A. 34 units
• B. 25.2 units
• C. 12.6 units
• D. 27.8 units

10. Greta takes a cab ride along Avenue F and Avenue G. Jack takes a cab ride along Avenue H. How many miles shorter is Jack’s cab ride than Greta’s? Record your answer.