Geometry and Measurement - Geometric Shapes - Quiz 2

Triangle ABC has been plotted on a coordinate graph with the points A (-3, 1), B (-1, 3), and C (-1, 1). If the triangle is translated 5 units right and 2 units down, what are the new coordinates of point A?

(2, -1) Moving to the right means adding to the x value. Moving downward means subtracting from the y value.

A teacher wants her students to demonstrate mastery of combining and dissecting figures. Which of the following is the best activity to determine if they have mastered this concept?

A project where students determine the area of 10 oddly shaped objects they have encountered in the last week and describe the process. This allows students to demonstrate mastery both in the objects they choose and their approach to determining the area. This also relates math concepts to the real world.

Juan is 5 feet tall and casts a shadow that is 10 feet long. If the flagpole casts a shadow that is 30 feet long, how tall is the flagpole?

15 feet Since Juan and the flagpole are in the same setting, they are creating similar shapes. A proportion can be used. Juan is 5 feet tall and casts a 10 foot shadow, while the unknown height flagpole casts a 30 foot shadow. So, 5/10 = x/30. Rearranging, x = (5/10)30, or 15.

What is the volume of the triangular prism pictured?

60 in3 The volume of a prism is in general B*h. The base of this prism is a triangle. The area of a triangle is ½ × b × h. The area of the base is ½ × 3 × 4 = 6 and then it is multiplied by the heights so 6 × 10 = 60.

A tennis ball has a diameter of about 3 inches. The container that holds a stack of three such balls is a right cylinder with a circular base. What is the approximate volume, in cubic inches, of the container that holds three tennis balls?

64 To find the volume of a right cylinder with a circular base, the area of the base of the cylinder is multiplied by its height. The area of the base of this container is a circle and so the calculation for its area should follow the formula A = πr2, where A = the area of the circular base and r = the radius of the base. The radius of the circular base of the can should be approximately equal to (though slightly larger than) the radius of the tennis ball. The diameter of the ball is given as "about 3 inches". Because diameter is twice radius, the radius of the tennis ball must be approximately half of that amount, or about 1.5 inches. Therefore, the area of the base of the cylindrical can with a circular base can be calculated as A = π(1.5)2 = 2.25π ≈ 7.07 square inches. It was given that the can for the tennis balls fits a stack of three tennis balls. Therefore, the height of the can should equal the height of three 3-inch diameter balls stacked on top of each other: 3(3 inches) = 9 inches. Therefore, the height of the can must be about 9 inches. Now the volume of the container can be calculated by multiplying the area of the circular base, ~7.07 inches, with the height of the can, ~9 inches. 7.07(9) = 63.63 in³. This answer can be rounded to approximately 64 cubic inches for the best approximate answer to this question.

Which statement about a rectangular prism and a rectangular pyramid is true?

Only the pyramid has triangular faces. Prisms have rectangular faces while pyramids have triangular faces. A pyramid has one base and a prism has two bases that are parallel to each other. A prism and a pyramid are named by their bases.

Mrs. Nadir's students are great at determining the surface area of cubes. They struggle with determining the surface area of rectangular prisms. What should she do to help her students be successful?

Reinforce how to determine the area of rectangles and then procedurally add the areas of the faces of a block. This will ensure students know both how to determine the area of rectangles, and also shows the students where the surface area is coming from.

Which of the following triangles is congruent with the triangle shown above?

The three sides and the three angles of congruent triangles are exactly the same, although the triangles may have different orientations. In this case, the triangle has been rotated counterclockwise.

In the figure, which line represents a line of symmetry?

line m Line m is the line of symmetry in this sketch. If you were to fold the figure on line m, the two halves would match up perfectly - much like the wings of a butterfly. One half would become a reflection of the other half when folded on m. This is not true of any of the other lines.

Which terms best describe the triangle shown? Select all answers that apply.

right Right triangles contain a right (90 degree) angle. C scalene Scalene triangles have all sides of different length.