Question

32 and AD BC PBLD IS a trapezium in which ABLICD Show that (1) ДА - 20 (fi) 20 = 20 LC2D Фі) Апас Двро ( су v) Ас - Во​

Answer 1

Answer:

Step-by-step explanation:

Given ABCD is trapezium where AD=BC.

(i) To prove: ∠A=∠B

we can see that AECD is a parallelogram, so sum of adjacent angles =180  

o

 

→∠A+∠E=180  

o

 

→∠A+x=180  

o

 

→∠A=180  

o

−x=∠B

Hence proved.

(ii) To prove: ∠C=∠D

sum of adjacent angles in parallelogram is π, so  

→∠D∠C+180  

o

−2x=180  

o

 

→∠C+∠D=2x

Now

→∠B+∠C=180  

o

 

→180  

o

−x+∠C=180  

o

=0        ∠C=x, so  

                                                         ∠D=x

And,

∠C=∠D

Hence proved.

(iii) ΔABC=ΔBAD

→ side AB is common.

→AD=BC (given)

so the angle including both the sides is also same,

∠A=∠B. So

ΔABC=ΔBAD (By SAS congruent Rule)

Hence proved.

(iv) As ΔABC=ΔBAD

The third side of both triangles i.e. diagonals are equal AC=BD