Question

indicate the method you would use to prove the two △s ≅. if no method applies, enter
one\.
ll
ha
hl
la
none

Explanation:

• HA (Hypotenuse - Angle):
• For right - angled triangles, the HA (Hypotenuse - Angle) congruence criterion states that if the hypotenuse and an acute angle of one right - angled triangle are equal to the hypotenuse and an acute angle of another right - angled triangle, then the two right - angled triangles are congruent.
• In the given triangles:
• Both are right - angled triangles (they have a \(90^{\circ}\) angle).
• The hypotenuse (marked with a cross) is equal for both triangles (by the marking).
• The non - right angle (\(45^{\circ}\)) is equal for both triangles.
• LL (Leg - Leg): This criterion is for when the two legs of a right - angled triangle are equal to the two legs of another right - angled triangle. But we are not given information about the legs.
• HL (Hypotenuse - Leg): This criterion is for when the hypotenuse and a leg of a right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle. But we are not given information about a leg.
• LA (Leg - Angle): This is not a standard congruence criterion for right - angled triangles in the common sense (the standard ones are LL, HA, HL).

Answer:

HA