Title: Unit 7 Quiz
Course: Technical Math for Industry

Q: Identify all points and line segments in the picture below.
- Points: A, B, C, D

Line segments: (Incorrect. The number of points is correct, but you appear to have included any possible line segments that could be drawn, and not just the actual ones that are drawn.)
- Points: A, B, C, D

Line segments: (Incorrect. The choices named are all correct, but there are other line segments in this picture. You may not have realized that a ray could contain a line segment.)
- Points: A, B, C, D

Line segments: (Correct. The four letters are used to label four points. The pairs of points A and B, A and C, and B and D are connected by line segments.)
- Points: A, B

Line segments: (Incorrect. The choices named are all correct, but there are other points and line segments in this picture. You may not have realized that a ray could contain a line segment. Also, every capital letter is a label for a point.)
A: Points: A, B, C, D

Line segments:

Q: Which angle is an acute angle?
- CPB (Correct. Acute angles measure less than , and this angle does.)
A: CPB
If wrong: Incorrect. Perhaps you have confused acute angles with right angles or did not notice the right angle symbol in the drawing. Acute angles measure less than .
If wrong: Incorrect. Perhaps you have confused acute with obtuse. Acute angles measure less than .
If wrong: Incorrect. Perhaps you have confused acute with obtuse. Acute angles measure less than .

Q: Which two statements are both true?
- and (Correct. The first pair of lines is perpendicular, as indicated by the right angle mark at their intersection. The second pair of lines is parallel because they are perpendicular to the same line.)
- and (Incorrect. Although one of the statements is true, the other one is not. Lines are known to be parallel if they have small double arrow symbols or if they are perpendicular to the same line. Lines are known to be perpendicular if they have a right angle mark at their intersection.)
- and (Incorrect. Although one of the statements is true, the other one is not. Lines are known to be parallel if they have small double arrow symbols or if they are perpendicular to the same line.)
- and (Incorrect. Although one of the statements is true, the other one is not. Lines are known to be perpendicular if there is a right angle mark at their intersection.)
A: and

Q: Find the measure of .
A: (a choice with no text)
If right: Correct. is a straight angle, so it measures . The four angles along this straight angle have measures that total . So:
If wrong: Incorrect. You may have correctly found the sum of the three angles' measures, but then subtracted that sum from 180 incorrectly.
If wrong: Incorrect. Perhaps you thought that was the same size as . The four angles along the straight angle have measures that total . Find the sum of the three given angles and then subtract that sum from 180.
If wrong: Incorrect. You may have mistakenly believed that measured . You need to use the fact that, because is a straight angle, it measures . The four angles along this straight angle have measures that total . Use the three given measures to find the fourth.

Q: Look at and in the image below.

Which of the following is the best description for this pair of angles?
- acute (Incorrect. Each angle is acute. However, the word ''acute'' does not describe the pair of angles.)
- supplementary (Incorrect. Perhaps you confused the definition of supplementary angles with the definition of complementary angles.)
- right (Incorrect. The pair of angles together form a single angle. That single angle is a right angle. However, the word ''right'' does not describe the pair of angles.)
- complementary (Correct. The two given angles form a right angle, so their measurements will add up to . This makes them complementary angles.)
A: complementary

Q: How would the following triangle be classified?
- scalene acute (Incorrect. The triangle offers no indication that any of the sides are congruent, so it is scalene. However, the triangle shows a right angle with a corner mark.)
- scalene right (Correct. The triangle shows a right angle with a corner mark and offers no indication that any of the sides are congruent, so it is classified as a scalene right triangle.)
- isosceles acute (Incorrect. The triangle is neither isosceles nor acute. The triangle shows a right angle with a corner mark, and offers no indication that any of the sides are congruent. Classify the triangle according to this information.)
- isosceles right (Incorrect. The triangle shows a right angle with a corner mark, but offers no indication that any of the sides are congruent. Classify the triangle according to this information.)
A: scalene right

Q: Which statement about the two triangles is correct?
- is not similar to , because , while . (Incorrect. It is the ratio between the side lengths, and not the difference between them, that is important in determining if triangles are similar.)
- You cannot tell if the triangles are similar because the angles are not given. (Incorrect. While it is true that you can use the angles to determine if two triangles are similar, there is another way to find this out. You need to look at the relationship between the corresponding sides.)
- is congruent to (Incorrect. Congruent triangles must be the same size and shape. These two triangles have the same shape, but has a larger size, so the triangles are not congruent.)
- ~ because (Correct. The corresponding sides of the two triangles are proportional, so the two triangles are similar.)
A: ~ because

Q: The two triangles below are similar because and .

Which option lists the other corresponding sides and angles?
- , , , , and (Incorrect. You identified the sides and the angles on the left with sides and angles on the right, but only the sides AC and HF are corresponding parts. The information in the problem tells you that A and H are corresponding angles, and also that B and G are corresponding angles. Therefore, C and F are corresponding angles. You will find corresponding sides opposite corresponding angles.)
- , , , and (Correct. Because A and H are corresponding angles, the sides opposite them are corresponding. So . Because B and G are corresponding angles, the sides opposite them are corresponding. So Because two pairs of corresponding angles have the same measures ( and ), the third pair of corresponding angles must be congruent. So , and therefore .)
- , , , and (Incorrect. You identified the sides on the left with each other and the sides on the right with each other, but these are not corresponding sides. You will find corresponding sides opposite corresponding angles.)
- , , ,  and (Incorrect. You correctly identified the corresponding sides. However, the angles on the left that you matched with the angles on the right are not corresponding angles. The information in the problem tells you that A and H are corresponding angles, and also that B and G are corresponding angles.)
A: , , , and

Q: Triangles FIM and LAK below are similar, and .

What is the length of ?
- 10 (Incorrect. You may have thought that because 12 is 4 more than 8, LA would be 4 more than 6. However, in similar triangles, side lengths are proportional. corresponds to , and corresponds to . Now set up the correct proportion and solve.)
- 16 (Incorrect. Perhaps you set up the correct proportion: but then solved it incorrectly. You should cross-multiply first.)
- 9 (Correct. Let x represent the unknown side. Set up a proportion of corresponding sides:)
- 4 (Incorrect. It appears that you set up the proportion incorrectly. corresponds to , and corresponds to . Now set up the correct proportion and solve.)
A: 9

Q: A flashlight is projecting a triangle onto a wall, as shown below.

The original triangle and its projection are similar. What is the missing length n on the projection?
- 30 (Correct.)
- 19.2 (Incorrect. You mixed up the corresponding sides when setting up the proportion. In this picture, the bases 24 and n are corresponding sides. The vertical sides 16 and 20 are corresponding as well. Set up the proportion and solve.)
- 13.3 (Incorrect. You mixed up the corresponding sides when setting up the proportion. In this picture, the bases 24 and n are corresponding sides. The vertical sides 16 and 20 are corresponding as well. Set up the proportion and solve.)
- 28 (Incorrect. You may have added 4 to 24, because 20 is 4 more than 16. This is not the correct way to find a missing side in a similar triangle. In this picture, the bases 24 and n are corresponding sides. The vertical sides 16 and 20 are corresponding as well. Set up a proportion and solve.)
A: 30

Q: Find the length of the hypotenuse in the following right triangle.
- 625 (Incorrect. You probably correctly applied the Pythagorean Theorem, but then forgot to take the square root. You need to solve for c.)
- 23.0 (Incorrect. You probably used the number 24 as the length of the hypotenuse instead of one of the legs. A proper use of the Pythagorean Theorem will give you . Solve for c.)
- 25 (Correct.)
- 31 (Incorrect. It appears that you just added the two leg lengths. You need to use the Pythagorean Theorem: . Substitute the values and and then solve for c.)
A: 25

Q: Troy is building a ramp for his toy cars. The plank he is using for the ramp is 8 feet long and is placed on a 2-foot-high box.

How far from the box is the bottom edge of Troy's ramp?
- 60 (Incorrect. You may have correctly used the Pythagorean Theorem to get , but you did not completely finish solving for b.)
- 6 (Incorrect. It appears that you just subtracted the 2 from the 8. The ramp is the hypotenuse of a right triangle. You need to use the Pythagorean Theorem:)
A: (a choice with no text)
If wrong: Incorrect. It appears that you used the Pythagorean Theorem with 2 and 8 as the legs. However, the ramp is the hypotenuse of the right triangle. The correct equation to use is:
If right: Correct. The ramp is the hypotenuse of a right triangle. Use the Pythagorean Theorem:

Q: Quadrilateral RSTQ is a parallelogram.

Which of the following relationships must be true?
A: (a choice with no text)
If wrong: Incorrect. Opposite sides and opposite angles in a parallelogram are congruent. Because and are adjacent sides in parallelogram RSTQ, they are not necessarily congruent.
If right: Correct. Opposite sides and opposite angles in a parallelogram are congruent. Because and are opposite angles in parallelogram RSTQ, they are congruent.
If wrong: Incorrect. Opposite sides and opposite angles in a parallelogram are congruent. Because and are adjacent angles in parallelogram RSTQ, they are not necessarily congruent.
If wrong: Incorrect. Opposite sides and opposite angles in a parallelogram are congruent. Because and are adjacent sides in parallelogram RSTQ, they are not necessarily congruent.

Q: Find the perimeter, in inches, of the parallelogram.
- 40 (Correct. Opposite sides of a parallelogram have the same lengths, so use the formula to find the perimeter.)
- 60 (Incorrect. You multiplied the base of the parallelogram by its height instead of finding the sum of the lengths of the four sides.)
- 20 (Incorrect. You added only the two given side lengths of the parallelogram, but you need to add all four side lengths.)
- 24 (Incorrect. You added the three measurements labeled on the figure, instead of finding the sum of the lengths of the four sides of the parallelogram.)
A: 40

Q: An abstract sculpture in the form of a triangle has a base of 11 meters and a height of 12 meters. Find the area of the triangle.
- 23 square meters (Incorrect. You added the base and the height of the triangle instead of using the formula to find the correct area.)
- 132 square meters (Incorrect. You multiplied the base times the height of the triangle. You need to multiply that product by to find the area.)
- 11.5 square meters (Incorrect. You added the base and the height of the triangle and multiplied the sum by instead of using the formula to find the correct area.)
- 66 square meters (Correct. The formula for the area of a triangle is: Substitute the values and : The area of the triangle is 66 square meters.)
A: 66 square meters

Q: Find the area of the figure below, formed from a triangle and a parallelogram.
- 144 square millimeters (Incorrect. You may have forgotten the in the formula for the area of a triangle.)
- 120 square millimeters (Incorrect. You may have forgotten the in the formula for the area of a triangle and also mistakenly multiplied the area of the parallelogram by , thinking of the formula for a triangle or a trapezoid.)
- 72 square millimeters (Incorrect. You may have mistakenly multiplied the area of the parallelogram by , thinking of the formula for a triangle or a trapezoid.)
- 96 square millimeters (Correct. Add the areas of the triangle and the parallelogram. Area of the triangle: Area of the parallelogram: The total area of the figure is square millimeters.)
A: 96 square millimeters

Q: Which letter on the diagram below represents a radius of the circle?
- D (Incorrect. The letter D represents the circumference of the circle or the circle itself. A radius of a circle is a line segment from the center of the circle to a point on the circle.)
- C (Correct. A radius of a circle is a line segment from the center of the circle to a point on the circle. The line segment labeled with the letter C is a radius.)
- B (Incorrect. The letter B represents a diameter of the circle. A radius of a circle is a line segment from the center of the circle to a point on the circle.)
- A (Incorrect. The letter A represents the center of the circle. A radius of a circle is a line segment from the center of the circle to a point on the circle.)
A: C

Q: Find the circumference of a circle with a diameter of 20 centimeters. Round your answer to the nearest centimeter.
- 6 centimeters (Incorrect. You may have divided the diameter by , instead of multiplying by .)
- 63 centimeters (Correct. The circumference of a circle is given by the formula , with . In this circle, , so: Rounded to the nearest centimeter, the circumference of the circle is 63 centimeters.)
- 126 centimeters (Incorrect. You may have thought that the circumference equals . The formula for the circumference of a circle is or . In this circle, .)
- 31 centimeters (Incorrect. You multiplied by the radius of the circle, instead of multiplying it by the diameter.)
A: 63 centimeters

Q: A flying disc has a radius of 6 inches. What is the area of one side of the flying disc to the nearest square inch? Use 3.14 as an approximation for .
- 38 square inches (Incorrect. You used the formula for the circumference of a circle instead of the area.)
- 28 square inches (Incorrect. You may have thought that the diameter of the flying disc was 6 inches and divided the value by 2 before using the area formula. However, the radius of the flying disc is 6 inches.)
- 113 square inches (Correct. Use in the formula to find the area: Rounded to the nearest square inch, the area of one side of the flying disc is 113 square inches.)
- 452 square inches (Incorrect. You used the square of the diameter in the area formula instead of the square of the radius.)
A: 113 square inches

Q: Find the approximate area of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for .
- 86 square feet (Correct. The diameter of the circle equals the side length of the square. So the area of the square is square feet. Use the radius of the circle, , to find the area of the circle: square feet The area of the shaded region equals the area of the square minus the area of the circle. This is approximately square feet.)
- 214 square feet (Incorrect. After finding and using this to find the area of the circle, you probably used this number as the side length to find the area of the square. Then you subtracted in the wrong order. The side length of the square is 20. Find the area of the square and then subtract the area of the circle from this.)
- 314 square feet (Incorrect. You found the area of the circle. You need to subtract this from the area of the square to find the area of the shaded region.)
- 856 square feet (Incorrect. You probably found the area of the circle using 20 as the radius instead of 10, and then subtracted the area of the square. Find the approximate area of the circle with and then subtract this from the area of the square.)
A: 86 square feet

Q: Which of the following shapes has a circular base?
- cone (Correct. A cone is a solid figure with a single circular base, and a smooth, round face that diminishes to a single point.)
- rectangular prism (Incorrect. A rectangular prism has a rectangular base, not a circular base.)
- pyramid (Incorrect. A pyramid has a polygonal base, not a circular base.)
- cube (Incorrect. A cube has a square base, not a circular base.)
A: cone

Q: Which is the best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm? Use 3.14 for .
- 785 cubic millimeters (Incorrect. You may have used the correct formula for the volume of a cylinder, , but switched the values for the radius and the height. In this problem, and .)
- 1,570 cubic millimeters (Correct. The volume of a cylinder is . Substitute and into the formula: cubic millimeters)
- 523 cubic millimeters (Incorrect. You used the formula to find the volume, but this is the formula for a cone. Note that is the correct formula for a cylinder.)
- 157 cubic millimeters (Incorrect. You may have forgotten to square the radius in the formula for the volume of a cylinder. Note that is the correct formula for a cylinder.)
A: 1,570 cubic millimeters

Q: The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
- 780 (Incorrect. You found the volume of the rectangular prism and the volume of the hole shaped like a rectangular prism, but you added the two volumes instead of subtracting the volume of the hole from the solid.)
- 300 (Correct. First find the volume of the large rectangular prism: Then find the volume of the hole, shaped like a rectangular prism: Subtract the volume of the hole from the volume of the large rectangular prism: The volume of the solid is 300 cubic millimeters.)
- 60 (Incorrect. You may have thought to subtract the larger minus the smaller dimensions and then multiply them together. However, this will not give you the correct volume. You must separately use for the large prism and for the hole. Then subtract the larger volume minus the smaller one.)
- 540 (Incorrect. You found the volume of the rectangular prism, but did not subtract the volume of the hole that is going through the center of it.)
A: 300