Answer:
We can use HA and HL congruence theorems or SAS, ASA or AAS postulate as a reason forΔHEL ≅ ΔPME.
Step-by-step explanation:
In the given picture we can see that
In ΔHEL and ΔPME
EH=MP[side]
EL=ME[side]
∠H=∠P=90°[angle]
∠L=∠E[ acute angle]
∴ We can use either SAS or ASA/AAS congruency postulate such that
ΔHEL ≅ ΔPME
Or As these triangles are right angled triangle and
EH=MP[side]
EL=ME[side]
∠L=∠E[ acute angle]
∴ we can also use HL and HA congruence theorems such that ΔHEL ≅ ΔPME
HL theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
HA theorem states that if the hypotenuse and one acute angle of a right triangle are equal to the hypotenuse and one acute angle of another right triangle, then the triangles are congruent.
LL theorem states that if legs of a right triangle are equal to the legs of another right triangle, then the triangles are congruent.
We cannot use LL theorem as a reason as there is only one leg is equal to the leg of other triangle.
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