Question

abcd is a quadtrilateral in which all the four angles are equal. show that ab ii cd and ad ii bc

Answer 1

Proof

∡ A+∡B+∡Ç+∡D=360° [sum of the angles of a quadtrilateral=360° ]

=>∡A+∡A+∡A+∡A=360°

=>4*∡A=360°

=>∡A=90°

Again, ∡ A+∡B=180°

Therefore, ∡ A and ∡B are supplementary angle

so they are adjacent angles

∴ AD || BC [∵ there interior ∡ A +∡ B =180°.]

Similarly, angle∡A+∡D=180°

∴, angles ∡A and ∡D supplementary angle

so they are adjacent ∡

∴ AB || CD [∵ there interior angles ∡A + ∡B = 180°.]∵

hence it is proved that AB ||CD