Unit 5 Geometry Test

The height of the bigger window can be determined by comparing the measurements of the two rectangles. Since the rectangles represent similar windows, their corresponding sides are proportional. By using the given measurements, we can set up a proportion to find the height of the bigger window. Since 2.6 feet corresponds to 15.6 feet in the smaller window, and we are trying to find the height of the bigger window, we can set up the proportion 2.6/15.6 = x/4.6. Solving for x, we find that x is equal to 3.9 feet.

The values of x in the triangle are 8 degrees, 13 degrees, 16 degrees, and 29 degrees.

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When a cone is sliced vertically through the vertex, the resulting cross section will be a triangle. This is because the intersection of the plane with the cone forms a triangle shape. The base of the triangle is the circular base of the cone, and the two sides of the triangle are formed by the slanted surface of the cone converging at the vertex. Therefore, the correct answer is triangle.

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When a square pyramid is sliced by a plane perpendicular to its base, the resulting cross section will be a trapezoid. This is because the plane intersects the pyramid in a way that one side of the trapezoid is parallel to the base of the pyramid, while the other side is shorter and slanted. The shape does not form a square because the slanted side creates a shorter length.

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The cross section of a pyramid is the shape that is formed when the pyramid is cut by a plane parallel to its base. In this case, the cross section is a square because the pyramid is cut parallel to its base, resulting in a shape that has four equal sides and four right angles.

The side lengths 6 cm, 6 cm, and 4 cm could be used to make a triangle. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, 6 cm + 6 cm = 12 cm, which is greater than 4 cm. Similarly, 6 cm + 4 cm = 10 cm, which is greater than 6 cm. Therefore, these side lengths satisfy the triangle inequality theorem and can form a triangle.

The sum of the angles in a triangle is always 180 degrees. Therefore, if Chantel constructs a triangle with angle measures of 65 degrees and 38 degrees, the measure of the third angle can be found by subtracting the sum of the other two angles from 180 degrees. 180 - (65 + 38) = 77 degrees.

The value of x in the figures shown is 156 degrees.

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Based on the figure provided, it appears that the circle's diameter is 63 cm. The circumference of a circle can be calculated using the formula C = πd, where d is the diameter. Therefore, the circumference of this circle would be 3.14 * 63 = 198 cm.

The height of the lamp post can be determined by setting up a proportion between the height of the street sign and its shadow, and the height of the lamp post and its shadow. Since the street sign is 9 feet tall and casts a 12-foot shadow, the ratio of height to shadow is 9:12. Using this ratio, we can find the height of the lamp post by setting up the proportion 9/12 = x/24, where x represents the height of the lamp post. Solving for x, we find that x = 18 feet. Therefore, the height of the lamp post is 18 feet.

In the figure shown, x is the angle opposite to the angle labeled 17 degrees. According to the properties of a triangle, the sum of all angles in a triangle is 180 degrees. Since the angle labeled 17 degrees is opposite to x, we can conclude that x must also be 17 degrees.

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The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius. In this case, the radius is given as 4 in. Plugging this value into the formula, we get C = 2π(4) = 8π. To find the numerical value, we can use an approximation of π as 3.14. Therefore, C ≈ 8(3.14) = 25.12 in.

To find the length of the third side of triangle XYZ, we can use the proportion of the corresponding sides of the two similar triangles. Since triangle ABC is similar to triangle XYZ, the corresponding sides are in proportion. Therefore, we can use the proportion of the lengths of the sides of the two triangles to find the length of the third side of triangle XYZ.

To find the total surface area of a right triangular prism, we need to calculate the area of each face and then add them up. The prism has two triangular faces and three rectangular faces. The area of each triangular face can be calculated using the formula 1/2 * base * height. The area of each rectangular face can be calculated by multiplying the length and width. Once we have calculated the area of each face, we can add them up to find the total surface area of the prism.

The size of the dining room rug is 216 inches by 222 inches. To find a rug that is similar in shape, we need to find a rug with a similar ratio of length to width. The ratio of length to width for the dining room rug is 216/222, which simplifies to 0.973. Among the given options, the rug with the closest ratio is 72 in by 74 in, which has a ratio of 0.973. Therefore, the 72 in by 74 in rug would be similar in shape to the dining room rug.

The scale of 1 inch: 8 feet means that 1 inch on the scale drawing represents 8 feet in real life. If the actual length of the classroom is 36 feet, we can calculate the length in the scale drawing by dividing 36 by 8. This gives us 4.5 inches, which is the length of the classroom in the scale drawing.

The area of a circle can be calculated using the formula A = πr^2, where A is the area and r is the radius. In this case, the diameter is given, so we can divide it by 2 to find the radius. The radius is 18/2 = 9 feet. Plugging this value into the formula, we get A = π(9^2) = 81π square feet. Since we are asked for an approximate answer, we can use the approximation π ≈ 3.14. Multiplying 81 by 3.14, we get approximately 254 square feet.

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The approximate area of one side of the coin can be calculated using the formula for the area of a circle, which is A = πr^2. Given that the radius of the coin is 26.5 millimeters, we can substitute this value into the formula to find the area.

Based on the given scale drawing, the area of the actual flower bed will be 96 square feet.

If Josh constructs a different triangle with angles measuring 54 degrees, 23 degrees, and 103 degrees, he will find that any other triangle he constructs with those angle measures will be similar to his original triangle. This is because triangles with the same angle measures are always similar, meaning they have the same shape but possibly different sizes. Therefore, no matter how Josh constructs a triangle with those angle measures, it will always have the same shape as his original triangle.

After cutting out the two circles, the remaining board will have an area of 15.5 square inches.