Question

ABCD is a parallelogram, ADEF and AGBH are two squares. Prove that FG=AC.​

Answer 1

Answer:

Step-by-step explanation:

Note: Please REPLACE AFG with F A G as spell checker considers F A G as inappropriate word.

Given,

ABCD is a parallelogram. ADEF and AGBH are the two squares.

Firstly,

AB = CD  ( ∵ Opposite sides of parallelogram are equal)

Since AB || DC,

∠BAD + ∠ADC = 180° ---------- [1] (∵ Sum of adjacent angles of

                                                            parallelogram is 180°)

∠FAD + ∠BAD + ∠BAG + ∠AFG = 360°

90° + ∠BAD + 90° + ∠AFG = 360°°

∠BAD + ∠AFG = 180° ---------------------- [2]

From [1] and [2]

∠BAD + ∠AFG = ∠BAD + ∠ADC

∠AFG = ∠ADC

Now in ΔAFG and ΔADC

AF = DA,

∠AFG = ∠ADC

AG = DC

∴ ΔAFG ≅ ΔADC ( By Side-Angle-Side Method)

∴ FG = AC.