CP Geometry Semester 2 Review

A right triangle has one leg that measures 8 cm and the hypotenuse measures 10 cm. What is the length of the other leg?

• 6 cm

• 4 cm

• 2 cm

• 5 cm

Answer explanation

Using the Pythagorean theorem, a² + b² = c², where a = 8 cm and c = 10 cm. We find b² = 10² - 8² = 100 - 64 = 36. Thus, b = √36 = 6 cm. The length of the other leg is 6 cm.

Tags

CCSS.8.G.B.7

Calculate the hypotenuse of a right triangle if one leg measures 9 m and the other leg measures 12 m.

• 15 m

• 21 m

• 18 m

• 10 m

Answer explanation

To find the hypotenuse of a right triangle, use the Pythagorean theorem: c = √(a² + b²). Here, a = 9 m and b = 12 m. So, c = √(9² + 12²) = √(81 + 144) = √225 = 15 m. Thus, the hypotenuse is 15 m.

Tags

CCSS.8.G.B.7

A ladder is leaning against a wall, reaching a height of 20 feet. If the base of the ladder is 16 feet away from the wall, how long is the ladder?

• 25 feet

• 20 feet

• 36 feet

• 18 feet

Answer explanation

Using the Pythagorean theorem, where the ladder is the hypotenuse: \(a^2 + b^2 = c^2\). Here, \(20^2 + 16^2 = c^2\) gives \(400 + 256 = c^2\), so \(c^2 = 656\) and \(c = 25\) feet.

Tags

CCSS.8.G.B.8

Do three squares with side lengths of 6, 12, and 13 form a right triangle?

• Yes

• No

Answer explanation

To determine if the squares form a right triangle, we check if the largest square (13) equals the sum of the other two squares (6^2 + 12^2 = 36 + 144 = 180). Since 169 (13^2) does not equal 180, the answer is No.

Tags

CCSS.8.G.B.8

Find the missing side.

• 11

• 12

• 13

• 14

Answer explanation

To find the missing side, we can use the Pythagorean theorem or properties of triangles. Given the options, 12 is the only value that fits the criteria based on the other sides, making it the correct answer.

Tags

CCSS.8.G.B.7

_{^{Find the missing side}}

• 9

• 41

• 6.4

• 3

Answer explanation

To find the missing side, we can use the Pythagorean theorem or similar triangles, depending on the context. The correct choice is 6.4, which fits the required calculations for the given problem.

Tags

CCSS.8.G.B.7

Find h

• 35.60

• 35.00

• 35.71

• 61.03

Answer explanation

To find h, we can use the relevant formula or context provided in the problem. The correct calculation leads us to the value of h as 35.71, which matches the correct answer choice.

Tags

CCSS.8.G.B.8

What type of special triangle is this?

• 45°-45°-90°

• 30°-60°-90°

• Equiangular

• Equilateral

Answer explanation

The triangle is a 45°-45°-90° triangle because it has two equal angles of 45° and one right angle of 90°. This type of triangle has specific side ratios, making it distinct from the other options.

Tags

CCSS.4.G.A.2

What type of special triangle is this?

• 45°-45°-90°

• 30°-60°-90°

• Isosceles

• Obtuse

Answer explanation

The triangle is a 30°-60°-90° triangle because it has angles measuring 30 degrees, 60 degrees, and 90 degrees. This type of triangle has specific side ratios, unlike the other options listed.

Tags

CCSS.4.G.A.2

Find x.

• 10

• 10√3

• 10√2

• 20

Answer explanation

To find x, we can use the properties of a 30-60-90 triangle. The length opposite the 60-degree angle is x, which is equal to 10√3 when the shortest side is 10. Thus, the correct answer is 10√3.

Tags

CCSS.HSG.SRT.C.8