Question

If non parallel sides of a trapezium are equal then it is

Answer 1

≡QUESTION≡

If non parallel sides of a trapezium are equal then it is                  

                                                       

║⊕ANSWER⊕║

If non parallel sides of a trapezium are equal then it is cyclic.

PROOF

Given: ABCD is a trapezium where AB||CD and AD = BC

To prove: ABCD is cyclic.

Construction: Draw DL⊥AB and CM⊥AB.

Proof: In ΔALD and ΔBMC,

AD = BC (given)

DL = CM (distance between parallel sides)

∠ALD = ∠BMC (90°)

ΔALD ≅ ΔBMC (RHS congruence criterion)

⇒ ∠DAL = ∠CBM (C.P.C.T) (1)

Since AB||CD,

∠DAL + ∠ADC = 180° (sum of adjacent interior angles is supplementary)

⇒ ∠CBM + ∠ADC = 180° (from (1))

⇒ ABCD is a cyclic trapezium (Sum of opposite angles is supplementary)

                                                         

Answer 2

Answer:

ok

Step-by-step explanation:

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