What can you say about the hypotenuse of the two triangles?
Both are correct. Explanation: See solution.
Practice makes perfect
Let's first explain the two theorems:
HL Congruence Theorem: If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.
SSS Congruence Theorem: If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Examining the diagram, we see that the two right triangles, â–ł JKL and â–ł LMJ, have the same hypotenuse, JL. By the Reflexive Property of Congruence, we can claim that the hypotenuses are congruent.
Next, by separating the two triangles, it becomes easier to see your cousin's and friend's points of view. Note that we will erase some parts of the diagram above depending on which point of view we are considering.
As we can see, congruence can be proved by both theorems. Therefore, your cousin and friend are both correct.
