geometry

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ethan3

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Using the diagram, prove that triangleOPQ is congruent to triangleTRS. Name any theorems used.

O is at the right angle of the triangle

OP is the base

PQ is the hypotenuse

Then, T is the right angle of the triangle

TS is the base

RS is the hypotenuse
 
Hello, ethan3!

Using the diagram, prove that: .\(\displaystyle \Delta OPQ \cong \Delta TRS.\)
Name any theorems used.

\(\displaystyle O\) is at the right angle of the triangle; \(\displaystyle OP\) is the base; \(\displaystyle PQ\) is the hypotenuse.

Then: \(\displaystyle T\) is the right angle of the triangle; \(\displaystyle TS\) is the base; \(\displaystyle RS\) is the hypotenuse.
Click to expand...

We need a better description of the diagram.

You have given us two right triangles . . . and that's it.

Code: 
    Q *
      **
      * *           R *
      *  *            * *
      *   *           *   *
      *    *          *     *
    O * * * * P     T * * * * * S


Without more information, how can they be congruent?

 
ethan3 said:
Using the diagram, prove that triangleOPQ is congruent to triangleTRS. Name any theorems used.

O is at the right angle of the triangle

OP is the base

PQ is the hypotenuse

Then, T is the right angle of the triangle

TS is the base

RS is the hypotenuse
Click to expand...

We can't SEE the diagram, of course.

But, I'm guessing (based on MANY years of teaching geometry) that there might well be some parts of the triangles marked as congruent. If there aren't any parts marked congruent, then all you know for sure is that an angle (the right angle) in one triangle is equal to the corresponding angle in the other triangle.

Lacking any further information about what other parts of the two triangles might be congruent, I'd say that it is impossible to determine whether the triangles are congruent or not.
 
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