Question

Select all the true statements. Two parallel lines cut by a transversal. The transversal makes 4 angles with the top line. Angles 1 and 2 are above the line and angles 3 and 4 are between the lines. The transversal also makes 4 angles with the bottom line. Angles 5 and 6 are between the lines and angles 7 and 8 are below the bottom line. Between the lines, angles 3 and 6 are on opposite sides of the transversal and angles 4 and 5 are on opposite sides of the transversal. A. ∠3 ≅ ∠2 because they are alternate interior angles. B. m∠1 + m∠3 = 180 because they form a straight angle. C. ∠3 ≅ ∠6 because they are alternate interior angles. D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180. E. ∠1 ≅ ∠3 because they are vertical angles.

Answer 1

Answer:

A)False

B)True

C)True

D)True

Explanation:

Refer the attached figure .

We are supposed to find the true statements .

A)∠3 ≅ ∠2 because they are alternate interior angles.

False . ∠3 ≅ ∠2 because they are vertically opposite angles.

B. m∠1 + m∠3 = 180 because they form a straight angle.

True. Since ∠1 and ∠3 forms a linear pair

C)∠3 ≅ ∠6 because they are alternate interior angles.

True .When a  transversal intersects a pair of lines, alternate interior angles are formed on opposite sides of the transversal. If the pair of lines are parallel then the alternate interior angles are equal to each other.

D) D. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180.

True .

m∠1 + m∠3 = 180.

We know that ∠3 ≅ ∠6

So, ∠1 + ∠6= 180.

Supplementary angles are those whose sum is 180°.

So,∠1 and ∠6 are supplementary