Question

Using the information in the given diagram, state if:

Options

• AD = DC

• BD = DC

• CD bisects angle ACB

• angle CAD is greater than angle DAB

Answer 1

CD bisects angle ACB

Explanation:

From figure,

AD = DB = AC = BC = x (let)

In △ ADC and △ BDC,

⇒ AD = DB (Both equal to x)

⇒ AC = BC (Both equal to x)

⇒ CD = CD (Common side)

∴ △ ADC ≅ △ BDC (By S.S.S. axiom)

We know that,

Corresponding parts of congruent triangle are equal.

∴ ∠ACD = ∠BCD

∴ CD bisects angle ACB.