Question

Which pair of corresponding parts must be congurent in order to use HL Theorem?

Answer 1

We want to know which pair of corresponding parts must be congruent in order to use the HL Theorem.

We remember that the HL Theorem is used for right triangles, and it states that if two different right triangles have their hypotenuse and another side congruent, the triangles are congruent.

In this case, we have two triangles:

`\Delta ABC\text{ and }\Delta BCD`

and both triangles share the side BC, which is a leg of the triangle. Thus, both triangles have a congruent leg.

As we want to use the HL Theorem, we need also the hypotenuse to be congruent:

`\bar{AB}\cong\bar{DC}`

Thus, AB must be congruent with DC in order to use HL Theorem.