In △ ABC, ab = AC, ad ⊥ BC is at point D, and points E and F are the midpoint of AB and AC sides respectively. When △ ABC satisfies what conditions, the quadrilateral AEDF is a square

In △ ABC, ab = AC, ad ⊥ BC is at point D, and points E and F are the midpoint of AB and AC sides respectively. When △ ABC satisfies what conditions, the quadrilateral AEDF is a square

When △ ABC is an isosceles right triangle, the quadrilateral AEDF is a square to solve the problem: if △ ABC is an isosceles right triangle, then D is the midpoint of BC, BAC is 90 degrees, because D is the midpoint of BC, f is the midpoint of AC, DF is parallel to AB, so ∠ CFD = ∠ BAC = 90 ° so ∠ AFD = 90 ° because D is the midpoint of BC, e is the midpoint of AB, so de

In the triangle ABC, angle ACB = 90 degrees, points D and E are the midpoint of AC and ab respectively, point F is on the extension line of BC, and angle CDF = angle A,
Proof: quadrilateral decf is parallelogram

Because angle ACB = 90 degrees, points D and E are the midpoint of AC and ab respectively,
So CE = AE + be
So angle ECD = angle A
Because angle CDF = angle a,
So angle CDF = angle ECD
So DF is parallel to EC and △ DFC is equal to △ CED
So DF = EC
So the quadrilateral decf is a parallelogram

In the triangle ABC, ∠ ACB = 90 ° points D and E are the midpoint of AC and ab respectively, point F is on the extension line of BC, and tangent ∠ CDF = ∠ a
The quadrilateral decf is a parallelogram

Because points D and E are the midpoint of AC and ab respectively
So de parallel BC is also parallel CF
Because ∠ ACB = 90 ° point, e is the midpoint of AB respectively
So AE = CE
Therefore, a = ace
And because ∠ CDF = ∠ a
Therefore, CDF = ace
So DF is parallel to CE
So the quadrilateral decf is a parallelogram