Title: M3.1 Basic Geometric Concepts and Figures
Course: Technical Math for Industry > Section: Module 3.0: Geometry Concepts and Figures

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
Feedback: 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 .
Feedback: Incorrect. Perhaps you have confused acute with obtuse. Acute angles measure less than .
Feedback: Incorrect. Perhaps you have confused acute with obtuse. Acute angles measure less than .

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)
Feedback: 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:
Feedback: Correct. The ramp is the hypotenuse of a right triangle. Use the Pythagorean Theorem:

Q: Find the measure of .
A: (a choice with no text)
Feedback: Correct. is a straight angle, so it measures . The four angles along this straight angle have measures that total . So:
Feedback: Incorrect. You may have correctly found the sum of the three angles' measures, but then subtracted that sum from 180 incorrectly.
Feedback: 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.
Feedback: 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