Question

# In the given diagram, Find the value of DC.

- 5 cm
- 10 cm
- 15 cm
- 20 cm

Hint:

### A triangle is a closed, two-dimensional shape or polygon in mathematics that has the fewest sides. Three sides and three angles make up a triangle. The fact that a triangle's inside angles add up to 180 degrees is its most crucial characteristic. Here we have given We have to find the value of DC.

## The correct answer is: 10 cm

### It is believed that two triangles are comparable triangles,

- if the angles that correspond to them are equal.
- if the ratio or proportion of their corresponding sides is the same.

The four key factors that determine how similar two triangles are are:

- AAA criterion (Angle-Angle-Angle criterion)
- AA criterion (Angle-Angle criterion)
- SSS criterion (Side-Side-Side criterion)
- SAS Criterion (Side-Angle-Side criterion)

Now here we have given the figure, and we have also given .

In ∆AOB and ∆COD, we have:

- $∠AOB=∠COD$ (Vertlcally opposite angles)
- (Given).

So now as one angle and one side are similar, so according to SAS similarity criterion, $ΔAOB∼ΔCOD.$

So here we used the concept of similar triangles. If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Congruent triangles have the same shape and size but similar triangles may have a different size. The symbol "≅" is used to signify congruent triangles. So here the value of DC is 10 cm.

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