Fill up the blanks — task. Mathematics CBSE, Class 9.

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Answer variants:

$CY$ is perpendicular to

$AB$

CPCT

altitudes

perpendicular line segment

two

$\triangle ACY$

$\angle AXB = \angle AYC$

$BX$

$ACY$

Prove that the altitudes are

$BX$ and

$CY$ are equal if triangle

$ABC$ is isosceles with

$AB = AC$ .

Proof:

It is given that

$BX$ and

$CY$ are

of triangle

$ABC$ .

An altitude is a

An altitude is a perpendicular line segment drawn through the vertex of the triangle to the opposite side.

Here,

$CY$ is an altitude of

$AB$ , and

is an altitude of

$AC$ .

Hence,

and

$BX$ is perpendicular to

$AC$ .

To prove that the altitudes are equal, let us consider

and

$\triangle ABX$ .

Here,

$AB = AC$ [Given]

Also,

as the altitudes meet the sides at right angles.

Also,

$\angle A$ is common to both triangles

and

$ABX$ .

Here,

corresponding pairs of angles and one corresponding pair of sides are equal.

Thus by congruence criterion,

$\triangle ACY \cong \triangle ABX$ .

Since

$\triangle ACY \cong \triangle ABX$ , and by

the altitudes

$CY$ and

$BX$ are equal.

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