Measurement and Geometry

At the zoo, the aquarium is 36 feet north of the gift shop. The monkey habitat is 323 feet east of the gift shop.

What is the distance, in feet, from the aquarium to the monkey habitat?

• 287

• 321

• 325

• 359

Figure 1 is rotated 90º counterclockwise about the origin to form Figure 2.

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A square pyramid has a base that is 44 inches wide and a slant height of 77 inches. What is the surface area, in square inches, of the pyramid?

• 18

• 72

• 90

• 54

A rug has two quadrilaterals woven into its design. On a diagram, the smaller quadrilateral is labeled GHIJ. The

second quadrilateral, labeled KLMN , is a dilation of GHIJ . Quadrilateral GHIJ is similar to quadrilateral KLMN.

Select the two statements that must be true.

• Angle G is congruent to angle H.

• Angle G is congruent to angle K.

• If the length of side KL = 2GH, then 2MN = IJ.

• The sum of angles H and I is equal to the sum of angles K and L.

• The sum of angles G, H, and I is equal to the sum of angles K, L, and M.

In the 􀃒gure, lines j and k are parallel to one another. Line m intersects both parallel lines to create 8 numbered angles, none of which are right angles. Garrett measures angles 1 and 6 . He says the measure of angle 1 is 65° and the measure of angle 6 is 125°. Jennifer claims Garrett is incorrect.

Which statement could Jennifer use to prove her claim?

• Angles 1 and 4 are congruent, and the sum of the measures of angles 4 and 6 must be 180°.

• Angles 1 and 3 are congruent, and the sum of the measures of angles 3 and 6 must be 180°.

• Angles 1 and 7 are supplementary, and the sum of the measures of angles 6 and 7 must be 180°.

• Angles 2 and 6 are supplementary, and the sum of the measures of angles 1 and 2 must be 180°.

Triangle ABC and triangle A'B'C' are shown on the coordinate plane.

Which sequence of transformations maps triangle ABC onto triangle A'B'C'?

• a rotation of 180 degrees and then a translation left 1 unit

• a translation left 5 units and then a reflection over the x-axis

• a reflection over the y-axis and then a translation down 8 units

• a reflection over the x-axis and then a reflection over the y-axis

A pile of gravel is in the shape of a cone. The radius of the pile of gravel is 9 feet at the base. The height of the pile of gravel is 8 feet. What is the volume of gravel, in cubic feet, in the pile?

• 48π

• 72π

• 216π

• 648π

Three sides of a triangle measure 25 inches, 24 inches, and 7 inches.

Which statement about the side lengths is correct?

• A The side lengths create a right triangle, because 7 + 24 > 25.

• B The side lengths create a right triangle, because 7² + 24² = 25² .

• C The side lengths do not create a right triangle, because 7 + 24 ≠ 25.

• D The side lengths do not create a right triangle, because 7² + 24² > 25² .

Quadrilateral ABCD is translated to form quadrilateral A'B'C'D'. How can the translation of quadrilateral ABCD to quadrilateral A'B'C'D'be described using coordinates?

• (x − 7, y − 2)

• (x − 2, y − 7)

• (x − 2, y + 7)

• (x + 7, y − 2)