Given rs congruent to tu rs perpendicular to st tu perpendicular to uv t is the midpoint of rv prove triangle rst congruent to triangle tuv

Question

Triangle proof Given rs congruent to tu rs perpendicular to st tu perpendicular to uv t is the midpoint of rv prove triangle rst congruent to triangle tuv 

Answer 1

Regina, based on your description, it sounds like you'd have a picture something like this.

v

| \
|   \
|     \
|⌉      \

u--1---t

          | \

          |   \

          |     \

          |⌉      \

          s--1---r

To prove the two triangles congruent, you need to use the hypotenuse-leg theorem.

This theorem requires you to establish that both triangles are right triangles (which you can do because the segments are perpendicular to each other).

That their hypotenuses are equal (which you can do because t is the midpoint of vr, which means that vt and tr are equal, and vt and tr are the respective hypotenuses)

That one of the legs of each triangle are equal, (which ut and sr are).

I hope this helps.