Please help :)

Of the statements provided, only 4. The line ℓℓ passes through a midpoint of one side of Δ.Δ. must be true.

We can see this by drawing a diagram of the situation:

[asy] unitsize(0.8 cm);

pair A, B, C, D;

A = (0,0); B = (10,0); C = intersectionpoint(arc(A,10,0,180), arc(B,10,180,0)); D = (B + C)/2;

draw(A--B--C--cycle); draw(A--D);

label("A", A, SW); label("B", B, SE); label("C", C, NE); label("D", D, S); [/asy]

If line ℓ divides triangle △ABC into two congruent triangles, then it must pass through the midpoint of one of the sides of the triangle. In this case, line ℓ passes through the midpoint of side BC.

The other statements are not necessarily true. For example, triangle △ABC does not necessarily have two equal sides or two equal angles. Also, line ℓ does not necessarily have to be perpendicular to a side of the triangle.

Here are some examples:

If triangle △ABC is an isosceles triangle, then it will have two equal sides, but line ℓ may not pass through the midpoint of one of the sides.

If triangle △ABC is an equilateral triangle, then it will have two equal sides and two equal angles, but line ℓ may not pass through the midpoint of one of the sides.

If triangle △ABC is a right triangle, then line ℓ may be perpendicular to a side of the triangle, but it may not pass through the midpoint of one of the sides.

Therefore, the only statement that must be true is that line ℓ passes through the midpoint of one side of the triangle.