Prove that a line passing through mid point of non parallel side of a trapezium parallel to parallel sides bisect the other non parallel side.

If two equal chords of a circle intersect within the circle , Prove that the segments of one chordare separately equal to the corresponding segments of the other chord.

In the given figure, AB is the diameter of the circle C (0,r) and the chord CD is equal to the radius OC. if AC and BD when produced intersect at O,prove that <AEB = 60 degree

Please help me in these sums. ASAP

Prove that a line passing through mid point of non parallel side of a trapezium parallel to parallel sides bisect the other non parallel side

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 ()

ΔALD ≅ ΔBMC (RHS congruence criterion)

⇒ ∠DAL = ∠CBM (By Cpct)  (1)

Since AB||CD,

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

⇒ ∠CBM + ∠ADC =  [from (1)]

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

 

@ AtulMohan123

Your Last statement is incomplete.

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