Geometry Question on Triangles

Question

Based on the given information, can you conclude that ?QRS≅?TUV ? Explain.

Given: (QR) ≅(TU) ,(QS) ≅(TV) and <R = <U, prove ?QRS≅?TUV

 

 

 

Please show me how I should go about doing this! Thank you.

Answer 1

No, you can't conclude that the triangles are congruent.

 

What you have is the situation called "SSA" -- side-side-angle.  Two corresponding adjacent sides are congruent between the two triangles (have the same length), and one angle is congruent.  But the angle is opposite one of the two congruent sides.  That results in a situation where you can't prove the triangles to be congruent.

 

If the angle were BETWEEN the two sides, rather than opposite one of them, then you would have SAS (side-angle-side), and then you would be able to conclude that the triangles were congruent.

Answer 2

Draw 2 triangles with the information given but have one with <V acute and the other with <S obtuse. Do this by making SR shorter than UV. You'll see that the triangles aren't congruent.