Question

Please help it’s so important

Answer 1

Given:

In
`\Delta ABC, \overline{CA}=\overline{CB}`.

`\overline{CD}` is an altitude drawn from C to
`\overline{AB}`.

To prove:

`\overline{CD}` bisects
`\overline{AB}`.

Proof:

In
`\Delta ABC`,
`\overline{CD}` is an altitude drawn from C to
`\overline{AB}`.

It means,
`\Delta ACD\text{ and }\Delta BCD` are right angle triangles.

In
`\Delta ACD\text{ and }\Delta BCD`,

Hypotenuse :
`\overline{CA}=\overline{CB}` [Given]

Leg :
`\overline{CD}=\overline{CD}` [Common]

If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then by HL postulate both triangles are congruent.

`\Delta ACD\cong \Delta BCD` [HL postulate]

`\overline{AD}\cong \overline{BD}` [CPCTC]

`\overline{AD}=\overline{BD}`

It means, point D is the midpoint of
`\overline{AB}`.

So,
`\overline{CD}` bisects
`\overline{AB}`.

Hence proved.