Question

Why is MAE TON? HL HA LL

Answer 1

if the Hypotenuse and Leg of a right-triangle are congruent to corresponding parts of another right-triangle, then the triangles are congruent by HL.

HL theorem.

Answer 2

Answer:

1. HL: Hypotenuse-leg theorem.

Step by step explanation:

We have been given two right triangles and we are asked to find how our triangles are congruent to each other.

Since we know that if one leg and hypotenuse of a right triangle is congruent to leg and hypotenuse of another triangle then both triangles are congruent. We will use Pythagorean theorem to prove our answer.

In $\Delta MAE$, $(AM)^{2} =(AE)^{2} +(EM)^{2}$

In $\Delta TON$, $(OT)^{2} =(ON)^{2} +(TN)^{2}$

We have been given that $EM\cong TN$ and $AM\cong OT$, so by the definition of congruence EM=TN and AM=OT.

Upon using substitution we will get,

$(ON)^{2}+(TN)^{2} =(AE)^{2} +(EM)^{2}$

Since we are given that EM=TN,

$(ON)^{2}+(TN)^{2} =(AE)^{2} +(TN)^{2}$

Subtracting $(TN)^{2}$ from both sides of equation we will get,

$(ON)^{2}=(AE)^{2}$

$ON\cong AE$

We can see that our angle is congruent by SSS congruence. Therefore, we can see that $\Delta MAE\cong \Delta TON$ by Hypotenuse-leg theorem and first option is the correct choice.