Question

name fotemeh /21 math foundations 20 2.1 - 2.2 quiz multiple choice (1 mark each) identify the choice that best completes the statement or answers the question. place answers in the boxes at the bottom of the page. 1. which pairs of angles are equal in this diagram? a. a = b, c = d, and e = f b. a = e, c = g, and b = f c. a = c, e = f, and h = h d. a = e, b = d, and c = g 2. in which diagram(s) is ab parallel to cd? 1 2 a. choice 1 only b. choice 2 only c. choice 1 and choice 2 d. neither choice 1 nor choice 2 3. which statement about the angles in this diagram is false? a. ∠b = 50° b. ∠c = 50° c. ∠e = 130° d. ∠f = 62° 4. which statement about the angles in this diagram is false? a. ∠e+∠a = 180° b. ∠d+∠g = 180° c. ∠b+∠d = 180° d. ∠f+∠c = 180° 5. which angle property proves ∠pyd = 90°? a. corresponding angles b. alternate interior angles c. alternate exterior angles d. supplementary angles 6. in which diagrams are two lines parallel? 1 2 a. choice 2 only b. choice 1 only c. choice 1 and choice 2 d. neither choices 1 or 2 #1 #2 #3 #4 #5 #6 /6

Explanation:

Step1: Recall angle - pair relationships

For parallel lines, vertical angles are equal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Analyze Question 1

Vertical angles are equal. In the given diagram, \(a = e\), \(b = d\), and \(c = g\) because they are vertical angles. So the answer to Question 1 is d.

Step3: Analyze Question 2

For two lines to be parallel, corresponding angles must be equal. In Choice 1, the corresponding angles are not equal. In Choice 2, the corresponding angles are equal. So \(AB\parallel CD\) in Choice 2 only, and the answer to Question 2 is b.

Step4: Analyze Question 3

Using the fact that the sum of angles in a triangle is \(180^{\circ}\) and linear - pair and vertical - angle relationships. \(\angle b=180^{\circ}- 130^{\circ}=50^{\circ}\), \(\angle c = 50^{\circ}\) (corresponding or vertical angles), \(\angle e = 130^{\circ}\) (vertical angle to the \(130^{\circ}\) angle). \(\angle f
eq62^{\circ}\), so the false statement is d.

Step5: Analyze Question 4

\(\angle f\) and \(\angle c\) are not supplementary in the given diagram. The sum of \(\angle c\) and \(\angle f\) is not \(180^{\circ}\). The false statement is d.

Step6: Analyze Question 5

\(\angle PYD = 90^{\circ}\) because of supplementary angles. \(\angle KYA=120^{\circ}\), and its supplementary angle \(\angle AYD = 60^{\circ}\), and since \(\angle DYZ = 30^{\circ}\), \(\angle PYD=90^{\circ}\) due to supplementary angles. The answer is d.

Step7: Analyze Question 6

In Choice 1, the corresponding angles are equal (\(88^{\circ}\)), so the two lines are parallel. In Choice 2, the corresponding angles are not equal (\(72^{\circ}
eq108^{\circ}\)), so the two lines are not parallel. The answer is b.

Answer:

1. d
2. b
3. d
4. d
5. d
6. b