Home
Class 9
MATHS
ABCD is a trapezium in which AB||CD and ...

ABCD is a trapezium in which `AB||CD` and `AD=BC`. Show that
(i)`/_A=/_B`
(ii) `/_C=/_D`
(iii) `triangle ABC ~==triangle BAD`
(iv) `"diagonal " AC = "diagonal " BD`

Text Solution

Verified by Experts

(i) Given,`AD = CE` (Opposite sides of parallelogram AECD)
Also, `AD = BC`
Therefore, `BC = CE`
`∠CEB = ∠CBE` (Angles opposite to equal sides in a triangle are equal)
`=>∠BAD + ∠CEB = 180°`
`=>∠BAD + ∠CBE = 180° ... (1)`
[Since, ∠CEB = ∠CBE]
Also,
...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

ABCD is a trapezium in which AB ll CD and AD=BC Show that (i) /_A=/_B (ii) /_C=/_D(iii) DeltaABC~= DeltaBAD (iv) diagonal AC=diagonal BD [Hint Extend AB and draw a line through C parallel to DA intersecting AB produced at E]

If ABCD is a quadrilateral in which AB|CD and AD=BC, prove that /_A=/_B.

D is a point on side BC of Delta ABC such that AD=AC. Show that AB>AD

ABCD is a quadrilateral in which AB=BC and AD =CD ,Show that BD bisects boht the angle ABC and ADC

ABC is an isoceless triangle in which AB=AC . AD bisects exterior /_PAC and CD|AB. Show that (i) /_DAC=/_BCA( ii) ABCD is a plarallelogram.

ABCD is a trapezium in which AB||CD and AB=2CD . It its diagonals intersect each other at O then ratio of the area of triangle AOB and COD is

ABC is a triangle in which AB=AC and D is a point on AC such that BC^(2)=AC xx CD .Prove that BD=BC .

In the given figure ABCD is a trapezium with AB || Dc and AD = BC prove that diagonal AC = diagonal BD