Spring 2025 Final Celebration! Geometry

A lighthouse casts a 140-foot shadow. A nearby lamppost that measures 6 feet 6 inches casts a 9-foot shadow. What is the height of the lighthouse?

• The height of the lighthouse is 101 feet 8 inches.

• The height of the lighthouse is 90 feet.

• The height of the lighthouse is 120 feet.

• The height of the lighthouse is 85 feet 4 inches.

Tags

CCSS.HSG.SRT.B.5

Find the measure of each interior angle of hexagon DEFGHI with ∠D, ∠E, ∠G, ∠H, ∠I, if m∠D = 6x, and m∠F = 3x. Show ALL work and be as thorough with your work and your answer(s) as possible.

• m∠D = m∠E = m∠G = m∠H = m∠I = 130.9°, m∠F = 65.4°.

• m∠D, m∠E, m∠H= m∠I = 150°, m∠F = 60°.

• m∠D = m∠E = m∠G = m∠H = m∠I = 100°, m∠F = 50°

• m∠D = m∠E = m∠G = m∠H = m∠I = 105°, m∠F = 30°.

Mr. Thompson is standing on top of a building that is 30 feet above the parking lot below. Mr. Thompson’s line of sight is 6 feet above the top of the building. Mr. Thompson must look downward 34° to see his car in the parking lot below. How far is his car from the base of the building? Round your answer to the nearest hundredth of a foot.

• The car is approximately 53.37 feet from the base of the building.

• The car is approximately 40.25 feet from the base of the building.

• The car is approximately 60.00 feet from the base of the building.

• The car is approximately 30.00 feet from the base of the building.

Tags

CCSS.HSG.SRT.C.8

If RZ is an angle bisector and m∠PRQ = 70°, find m∠PRZ.

• 13

• 140

• 35

• 70

Tags

CCSS.HSG.CO.C.9

Find PR if QY is a median.

• 5

• 9

• 18

• 32

Tags

CCSS.HSG.CO.C.10

If WX is a perpendicular bisector of QR, find b.

• 6

• 12

• 35

• 90

Tags

CCSS.HSG.CO.C.9

In the figure at the right ABCD is similar to WXYZ. If AD = 8, DC = 7, and WZ = 20, find YZ.

• 16

• 17.5

• 19

• 20.5

Tags

CCSS.HSG.SRT.A.2

Find the value of x.

• 8

• 9

• 12

• 16

Tags

CCSS.HSG.CO.C.9

A model of a 180-foot tall lighthouse is built to the scale of 1 inch : 15 feet. How tall is the model?

• 10 inches

• 12 inches

• 14 inches

• 16 inches

Tags

CCSS.7.G.A.1

In the figure, CF is an angle bisector, GB is a perpendicular bisector, m∠ACF = 2x+3, m∠DCF = 5x-18. Find the value of x.

• 15

• 30

• 7

• 3.5

Tags

CCSS.HSG.CO.C.9