Abcd is a trapezium with ab parallel to cd

Asked by admin @ 23/08/2021 in Math viewed by 361 People

ABCD is a trapezium in which AB is parallel to CD and AD is equal to BC. show that angle A is equal to angle B. angle C equal to angle D. triangle ABC is congruent to triangle BAD and diagonal AC equal to diagonal BD

Answered by admin @ 23/08/2021

Hi friend!

Construction: Draw a line through C parallel to DA

intersecting AB produced at E.

Proof:

AB||CD(given)

AD||EC (by construction)

So ,ADCE is a parallelogram

CE = AD

(Opposite sides of a parallelogram)

AD = BC (Given)

We know that ,

∠A+∠E= 180°

[interior

angles on the same side of the transversal AE]

∠E= 180° - ∠A

Also, BC = CE

∠E = ∠CBE= 180° -∠A

∠ABC= 180° - ∠CBE

[ABE is a straight line]

∠ABC= 180° - (180°-∠A)

∠ABC= 180° - 180°+∠A

∠B= ∠A………(i)

(ii) ∠A + ∠D = ∠B + ∠C = 180°

(Angles on

the same side of transversal)

∠A + ∠D = ∠A + ∠C

(∠A = ∠B) from eq (i)

∠D = ∠C

(iii) In ΔABC and ΔBAD,

AB = AB (Common)

∠DBA = ∠CBA(from eq (i)

AD = BC (Given)

ΔABC ≅ ΔBAD

(by SAS congruence rule)

(iv) Diagonal AC = diagonal BD

(by CPCT as ΔABC ≅ ΔBAD)

Hope this helps!

Abcd is a trapezium in which ab parallel cd

Asked by admin @ 12/08/2021 in Math viewed by 381 persons

ABCD is a trapezium in which AB is parallel to CD and AD is equal to BC. show that angle A is equal to angle B. angle C equal to …

Abcd is a trapezium with ab parallel to dc

Asked by admin @ 10/08/2021 in Math viewed by 296 persons

"Question 13 ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY). …

Diagonals of trapezium abcd with ab parallel to dc

Asked by admin @ 17/08/2021 in Math viewed by 312 persons

The diagonals of a trapezium ABCD with AB||DC intersect each other at point O. If AB = 2CD, find the ratio of the ares of triangle AOB and COD.

Abcd is an isosceles trapezoid with legs ab and cd and base bc

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 337 persons

abcd is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC s 4y-6 and the length of …

Draw a parallelogram abcd in which ab 6.5 cm

Asked by admin @ 23/08/2021 in Math viewed by 262 persons

Draw a parallelogram ABCD in which AB=6.5 cm , AD = 4.8 cm and angel BAD= 70° , measure its Diagonals.

In the figure ab and cd are common tangents

Asked by admin @ 20/08/2021 in Math viewed by 343 persons

In Fig. 9.13, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.

Ab and cd are common tangents to two circles

Asked by admin @ 20/08/2021 in Math viewed by 341 persons

AB and CD are common tangents to two circles of equal radii. prove that AB=CD

Two equal chords ab and cd of a circle

Asked by admin @ 17/08/2021 in Math viewed by 326 persons

Two equal chords AB and CD of a circle when produced, intersect at point P prove that PB is equal to PD.

Ab and cd are two chords of a circle

Asked by admin @ 16/08/2021 in Math viewed by 437 persons

AB and CD are two chords of a circle such that AB= 10cm CD=24cm and AB parallel CD the distance between AB and CD is 17cm. Find the radius of …

Ab and cd are two diameters of a circle

Asked by admin @ 13/08/2021 in Math viewed by 267 persons

In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If …