(Proofs)
Given: AR = AQ RT = QS Prove: RAT = QAS

Here is the image: https://media.glynlyon.com/o_geo_2009/4/page47a.gif
(I don't need the whole answer, just a push in the right direction)

I'm hoping to be able to use the Side Angle Side theorem or the Side Side Side theorem to prove this. All I need is a postulate or theorem to prove that another side/ angle is congruent other than the given?
(I'm going to sleep but it would be super amazing if someone answered this while I was gone!)

Question

(Proofs)
Given: AR = AQ RT = QS Prove: RAT = QAS

Here is the image: https://media.glynlyon.com/o_geo_2009/4/page47a.gif
(I don't need the whole answer, just a push in the right direction)

I'm hoping to be able to use the Side Angle Side theorem or the Side Side Side theorem to prove this. All I need is a postulate or theorem to prove that another side/ angle is congruent other than the given? 
(I'm going to sleep but it would be super amazing if someone answered this while I was gone!)

ganeshie8 · Answer

start wid whats given :-

It is given that AR = AQ. Since two sides are congruent ARQ is an isosceles triangle. <ARQ = <AQR cuz the base angles of isosceles triangle are congruent. .....

ganeshie8 · Answer

a pair of side and a pair of angle are proven congruent already. see if you can prove another pair of sides are congruent, then you can use SAS congruency to conclude that triangles are congruent.

anonymous · Answer

Is there any way to prove that AS=AT?

ganeshie8 · Answer

No. try the other sides : RT and QS

anonymous · Answer

I understand that two sides of the one triangle is equal to the other, and that it is the given. I need to know how to prove either the included angle is congruent, or the last side is congruent.

ganeshie8 · Answer

you're right

ganeshie8 · Answer

read my first reply once. there ive proven the included angle is congruent.

anonymous · Answer

I know it's an isosceles and that would make the base angles congruent but I need to prove it's an isosceles? (thank you for putting up with me)

ganeshie8 · Answer

it is also proven there, read it once again

ganeshie8 · Answer

It is given that AR = AQ. $\color{red}{\text{Since two sides are congruent}}$ ARQ is an isosceles triangle. <ARQ = <AQR cuz the base angles of isosceles triangle are congruent.

anonymous · Answer

Oh! I think I might get it! Thank you, I'll write out the proof in the morning but this was very helpful, I was looking at it as two overlapping trianlges, not one whole triangle.

ganeshie8 · Answer

yea first we need to look at the outer big triangle. then we need to look at two overlapping triangles for proving the third side :)