Question

measure of vertex angle of the tangle
Find the area of trapezium, ABCD & AB = 2cm &BC=CD DA Tom
Construct a triangle ABC in which BC = 7cm, B = 75° and AB.AC13cm
ABCD is a trapezium in which ABTICO and AD BC. Show that
1) ZA = B 11) 2C = 20
Prove mid-point theorem.
inn nf a triangle divides it into two triangles of equal area​

Answer 1

1)proof of mid point theorem,

given,

ABC is a triangle,D andE are the mid points of two sides of triangle ABC.

To prove,

DE//BC,DE=1/2BC

Construction,

produced a line from E to F,and join CF

proof,

In triangle ADE and triangle CFE,

AE=CE (E is the mid point of AC)

<AED=<CEF (vertically opposite angle)

DE=EF (E is the mid point of AC)

therefore, triangle ADE is congruent to triangle CFE,

AD=CF (By CPCT)

Now,

we can say that,

AD=DE ( D Is the mid point of AB)

we can say that,

CF=DE

So,CF//DE

Therefore,EBCF is a parallelogram

so,DE//BC

And,we know that,

DE=EF

Therefore, DE=1/2DF

DE=1/2BC. (Since DF=BC)

Hence,Proved

2)given,

ABC is a triangle,