Question

if an isosceles Trapezium ABCD AD=BC.If A=60°, DC=25cm and AD=20 cm. Find the length AB​

Answer 1

Answer:

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Step-by-step explanation:

Through B, draw a straight line parallel to AD which meets CD at E.

Now, since AB∥DE and AD∥BE,

∴ABED is a parallelogram.

Thus, ED=AB=18cm

As, BE∥AD and CD is a transversal,

∴∠BED=∠D=60  degree

(∵∠ABE=∠D).

Since, in an isosceles trapezium, the base angles are equal, ∠C=∠D=60  degree.

In ΔBEC, ∠BED+∠ECD+∠CBE=180 degree (Angle sum property of a triangle)

⇒60  degree +60  degree+∠CBE=180  degree

⇒∠CBE=180 degree - 120 degree

⇒∠CBE=60  degree

As the measure of ∠BEC=60  degree  

,∠ECB=60  degree

and ∠CBE=60  degree

,ΔCBE is an equilateral triangle, Thus

∴CE=BC=12cm(BC=AD=12cm)

Now, CE+ED=12+18

⇒DC=30cm