Point m is the midpoint of ab . through point m a line segment xy is drawn, so that both xa and yb are perpendicular to ab . prove that ay ≅ bx .

See the proof below

Step-by-step explanation:

Let the line AB be a straight line on the parallelogram.

A dissection of the line (using the perpendicular line X) gives:

AY ≅ BX

Another way will be using the angles.

The angles are equal - vertically opposite angles

Hence the line  AY ≅ BX (Proved)

AY = BX proved.

Step-by-step explanation:

See the diagram attached to the answer.

Given AM = MB and ∠BAX = ∠ABY = 90°

Now, between ΔAXM and ΔBYM,

(i) AM = BM {Given}

(ii) ∠XAM = ∠YBM {Given}

(iii) ∠AMX = ∠BMY {Opposite angles}

So, we can say that ΔAXM ≅ ΔBYM

Hence, AX = BY (1)

Now, between ΔABX and ΔABY,

(i) AB is common side.

(ii) AX = BY {Already proved} and

(iii) ∠BAX = ∠ABY {Given}

Therefore, ΔABX ≅ ΔABY.

Hence, BX = AY {Corresponding sides} (Proved)

question is incomplete.