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

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 =

bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-02-22T11:10:47+01:00

The reasons matched with their statements for the given triangle ABR in which RA = RB RS | | AB Prove: <1 = <2 below.

What is triangle?

A triangle is the polygon in a 2 dimensional plane which made of three sides and three interior angles.

Ii is given In the triangle [tex]\Delta ABR[/tex] that,

The line segment RA is equal to RB.

The line segment RS is parallel to AB.

The image of the triangle [tex]\Delta ABR[/tex] is attached below.

Lets match all the the reason with given statement one by one,

1)Line RS is perpendicular to AB and angle <1 = <2-As this statement is given in the problem. Thus it should be match with given statement.

2) ∠B=∠1- As the lines RS and AB is parallel and when the lines are parallel to each other, then the angle of them are equal.

3) ∠A=∠2-Angle A is the alternative angle of angle 2 and the alternative angle are always equal to each other.

4) ∠A=∠B- The angle A and B are equal, due to the substitution angle and given that <1 = <2.

5) RA=RB- If the two angle of a triangle is equal, then the opposite sides of it is equal.

The reasons matched with the statements given which is triangle ABR RA = RB RS | | AB Prove: <1 = <2 above.

Learn more about the triangle here;

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