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# Help with a Geometric Proof?

This is the only one I can't get... maybe im just not thinking. Here it is: Given: SY=SW, YT bisects SYW, and WR bisects SWY; Prove: Triangle RXY= Triangle TXW..here's a quick image i made: http://i15.tinypic.com/29wr8dy.jpg -any help is appreciated!

### 5 Answers

- jcss_003Lv 51 decade agoFavorite Answer
ok it's been a while since i've done a triangle proof (over 5 years)

we know the <rxy = < txw cause they are mirrors of one another (forgot the therom)

then as you label has it <1 + <YXW = 90 ((opposite angels theorm)

given that <4 + <yxw = 90

therefore <4 = <1

likewise <xtw + <rxt = 90

<rxt = <yxt

<yxt + <1 = 90

therefor <1 = <XTW

use the same argument for <4 = <YRX

and triangle YRX and triangle WXT are equal by AAA (angel angel angel)

also i'm not sure if since segments sy = sw that that would make R and T the middle points of each line and therefore you could do a different argument that way?!?!?!?

hope it helps

- Anonymous1 decade ago
Here are some hints rather than just giving you the answer.

To prove triangles equal you usually have to prove that two side lengths and one angle are the same in both OR two angles and the side length between them are the same in both. (It's nopt quite that simple but it will do for now.)

Now SY = SW tells you that triangle YSW is what type? What does that tell you about its angles?. The lines bisecting the angles at Y and S also tell you something. From this you can establish that the angles in WXT are the same as those in YRX. You now need to prove a side length the same (because one triangle could be bigger than the other even with the same angles) but I've got to go so good luck.

- Anonymous1 decade ago
<1 = <2 (Definition of bisect)

<3 = <4

<SYW = <SWY (isosceles triangle---congruent base <'s)

<SYW= <1 + <2 (Angle Addition)

<SWY= <3 + <4

Eventually, you find that <1 = <2 = <3 = <4

<RXY = <TXW (Vertical angles are congruent)

XY = XW (<2 = <3 so isosceles triangle)

Triangle RXY = Triangle YXW (ASA)

- hermannsLv 44 years ago
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