if two non parallel sides of a trapezium are equal prove that it is cyclic
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Answered by
547
Heya friend,!!
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)
Hope it helps u
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)
Hope it helps u
Answered by
340
Hi there!
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For solutions, Refer to the attached picture.
Regrets for handwriting _/\_
_______________________
Let's see some related topics :
⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.
⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.
⚫ Secant : A line intersecting a circle at any two points, is called secant.
⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.
_______________________
Thanks for the question !
☺️❤️☺️
_______________________
For solutions, Refer to the attached picture.
Regrets for handwriting _/\_
_______________________
Let's see some related topics :
⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.
⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.
⚫ Secant : A line intersecting a circle at any two points, is called secant.
⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.
_______________________
Thanks for the question !
☺️❤️☺️
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