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)
Your Last statement is incomplete.