Pythagorean Theorem, Angles, and Triangles

The diagram represents the side view of a roof in the shape of a right triangle.

Which measurement is closest to the length of the roof in feet?

• 5.1 ft

• 16.1 ft

• 26.0 ft

• 19.7 ft

Parallelogram PQRT is shown.

Which statement proves that parallelogram PQRT is a rectangle?

• 15² - 8² = TQ²

• 8 + 15 = TQ

• 15 - 8 = TQ

• 8² + 15² = TQ²

The perimeter of the triangle shown is 17x units. The dimensions of the triangle are given in units.

Which equation can be used to find the value of x?

• 17x = 30 + 7x

• 17x = 15 + 22x

• 17x = 7 + 30x

• 17x = 22 + 15x

The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closest to the length of this rectangle in feet?

• 9 ft

• 17 ft

• 12.4 ft

• 13.6 ft

In each diagram, line f is parallel to line g, and line t intersects lines f and g.

Based on the diagrams, which statement is true?

• The value of x is 42 because vertical angles sum to 90.

• The value x is 48 because alternate, interior angles are congruent.

• The value of x is 132 because corresponding angles sum to 180.

• The value of x is 96 because there are two pair of adjacent angles.

The manager of a car dealership wants to attach a rope with flags to the top of a pole and to a stake in the ground, as shown in the diagram.

Based on the diagram, what is the distance in feet from the top of the pole to the bottom of the stake?

• 45.5 ft

• 32.5 ft

• 22.5 ft

• 6.7 ft

The set designer for a play painted some background scenery on a large piece of plywood. He used a 13-foot-long pole to hold the piece of plywood upright, as shown in the diagram below.

What is h, the total height in feet of the piece of plywood?

• 12 ft

• 13.9 ft

• 14 ft

• 10 ft

The figures shown each have a set of parallel lines interested by a transversal.

Based on the figures, what are the measures x, y, and z in degrees?

• x = 30

• y = 30

• z = 60

• y = 60

• x = 120

The scatterplot shows the relationship between the weight in pounds and the age in weeks of a certain dog breed.

Based on the scatterplot, which is the best prediction of the weight in pounds of a dog that is 28 weeks old?

• 12 lb

• 75 lb

• 45 lb

• 105 lb

In each diagram, line x is parallel to line y, and line z intersects lines x and y.

Based on the diagrams, which statement is true about the value of a?

• The value of a is 53 because it is adjacent to an angle that is 53.

• The value of a is 37 because 90 - 53 = 37.

• The value of a is 127 because alternate, exterior angles are congruent.

• The value of a is 180 because 53 + 127 = 180.