Question

In ΔAOB and ΔCOD, ∠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

Given:

ΔAOB and ΔCOD 

∠B = ∠C

O is the midpoint of BC

AB = 3x units

CD = y + 2 units  

AO = x + 2 units 

DO = y units

Since O is the midpoint of BC, BO = OC.

By the given, ∠B = ∠C.

We can use the fact that triangles AOB and COD share these properties and solve for x and y by assuming congruency based on sides and angles.

The congruency and equality can be reasoned as:

AB = CD

3x = y + 2   ...(1)

AO = DO

x + 2 = y   ...(2)

From (2),

y = x + 2

Substitute y in (1):

3x = (x + 2) + 2

3x = x + 4

3x – x = 4

2x = 4

x = 2

Now y = x + 2

= 2 + 2

= 4

Hence, the values are:

x = 2

y = 4