Question

Match the reasons with the statements given. Given: triangle ABR RA = RB RS | | AB Prove: <1 = <2

Answer 1

Given the following statements
1. line RS || segment AB, ∠1=∠2
2. ∠B = ∠1
3. ∠A = ∠2
4. ∠A = ∠B
5. RA = RB

and the following reasons,
a) If lines ||, corresponding ∠'s are =
b) If two ∠'s of a triangle are =, sides opposite are =
b) If lines ||, alternate interior ∠'s =
c) Given
d) Substitution

we match the statements and the reasons to enable us prove the required proof.
         Statement                                                     Reason

1. line RS || segment AB, ∠1=∠2       Given
2. ∠B = ∠1                                         If lines ||, corresponding ∠'s are =
3. ∠A = ∠2                                         If lines ||, alternate interior ∠'s =
4. ∠A = ∠B                                        Substitution  [because we are given that
∠1=∠2]

5. RA = RB                                        If two ∠'s of a triangle are =, sides opposite are =