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:
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 [tex]\Delta MAE[/tex], [tex](AM)^{2} =(AE)^{2} +(EM)^{2}[/tex]
In [tex]\Delta TON[/tex], [tex](OT)^{2} =(ON)^{2} +(TN)^{2}[/tex]
We have been given that [tex]EM\cong TN[/tex] and [tex]AM\cong OT[/tex], so by the definition of congruence EM=TN and AM=OT.
Upon using substitution we will get,
[tex](ON)^{2}+(TN)^{2} =(AE)^{2} +(EM)^{2}[/tex]
Since we are given that EM=TN,
[tex](ON)^{2}+(TN)^{2} =(AE)^{2} +(TN)^{2}[/tex]
Subtracting [tex](TN)^{2}[/tex] from both sides of equation we will get,
[tex](ON)^{2}=(AE)^{2}[/tex]
[tex]ON\cong AE[/tex]
We can see that our angle is congruent by SSS congruence. Therefore, we can see that [tex]\Delta MAE\cong \Delta TON[/tex] by Hypotenuse-leg theorem and first option is the correct choice.
