Question

Can someone help me match these up? i know the given is number one I need help with the rest.

1. line RS || segment AB, ∠1=∠2


2.∠B = ∠1
3. ∠A = ∠2
4.∠A = ∠B
5. RA = RB

A:  If two ∠'s of a triangle are =, sides opposite are =
B: If lines ||, alternate interior ∠'s =
C: Given
D: Substitution
E: If lines ||, corresponding ∠'s are =

Answer 1

`C-1\\E-2\\B-3\\D-4\\A-5`

Answer 2

1-C, 2-E, 3-B, 4-D, 5-A

Explanation:

Firstly, from the figure, it is shown that line RS is parallel to the line segment AB and ∠1=∠2. Therefore, 1 matches with C.

Now, from the definition of parallel lines, the corresponding angles are always equal, therefore ∠B=∠1. Therefore, 2 matches with E.

Since, we are given that the lines are parallel, therefore by property of parallel lines, alternate angles are always equal. Therefore, ∠A=∠2. Hence, 3 matches with B.

Now, we know that ∠B=∠1 and ∠A=∠2, also that ∠1=∠2, therefore from these equations, ∠A=∠B. Hence, 4 matches with D.

If two angles of the triangle are equal that is ∠A=∠B, then the sides opposite to equal angles are always equal, therefore, RA=RB. Hence, 5 matches with A.