Only second pair of triangles can be proven congruent by Hypotenuse leg theorem(HL).
What is hypotenuse theorem leg(HL)?
The HL theorem leg (Hypotenuse theorem) states that the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
According to the given question.
We have three pairs of triangles.
For the first pair of triangles, both the triangles are not right angled triangles. So, we can't apply hypotenuse leg theorem.
For the second pair of triangles, both the pairs of triangles are right angled triangle and the hypotenuse and leg of one triangle is equals to the hypotenuse and leg of another triangle. Therefore, we can apply hypotenuse leg theorem for the second pair of triangles. So, the given triangles are congruent to each other.
For the third pair of triangles, both the triangles are right angled triangle but the only leg of one triangles is equal to the leg of another triangle. So, we can't apply Leg hypotenuse theorem for the second pair of triangles.
Hence, only second pair of triangles can be proven congruent by Hypotenuse leg theorem(HL).
Find out more information about hypotenuse leg theorem here:
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