Question

In triangleAOB and triangleCOD, B=C and O is the
midpoint of BC. Find the values of x and y if
AB = 3x units, CD = y + 2 units, AO = x + 2
units, DO = y units.​

Answer 1

Answer:

Step-by-step explanation:

n ∆AOB and ∆COD,

⟨B = ⟨C .

And O is the midpoint of BC .

BO = CO

Let, According to the question

AB = 3x units

CD = y + 2 units

AO = x + 2 units

DO = y units

TO FIND

The value of x and y .

SOLUTION

<B=<c [Given]

In the figure,

AB || CD and BC be line which intersect the two parallel lines .

<A=<D [Alternate angles]

AD line and BC line intersect each other at O .

<AOB=<COD [Opposite angles]

Now, in ∆AOB and ∆COD,

⟨A = ⟨D

⟨AOB = ⟨COD

⟨C = ⟨B

☃️ Hence, TRIANGLE AOB CONGRUENT TRIANGLE COD [AAA criteria]

SO,

=AB=DC

=3 x =Y+2

=3 x-Y=2----------[1]

and

=A O=DO

=X+2=Y

=X-Y= -2----------------[2]

Now, Equation (1) - Equation (2),

=> 3x - y - (x - y) = 2 - (-2)

=> 3x - y - x + y = 2 + 2

=> 2x = 4

=> x = 4/2

X=2

⚡ Put the value of “ x = 2 ” in equation (2), we get

=> 2 - y = -2.

=> y = 2 + 2

Y=4

The value of “x” is 2 and the value of “y” is 4 .