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

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Answer variants:

right angles

corresponding pair of sides

opposite side

\(CY\) is perpendicular to \(AB\)

\(\triangle ABX\)

\(AC\)

\(BX\) and \(CY\)

\(\triangle ACY \cong \triangle ABX\)

\(ACY\)

Prove that the altitudes are \(BX\) and \(CY\) are equal if triangle \(ABC\) is isosceles with \(AB = AC\).

Proof:

It is given that

are altitudes of triangle \(ABC\).

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

Here, \(CY\) is an altitude of \(AB\), and \(BX\) is an altitude of

Hence,

and \(BX\) is perpendicular to \(AC\).

To prove that the altitudes are equal, let us consider \(\triangle ACY\) and

Here, \(AB = AC\) [Given]

Also, \(\angle AXB = \angle AYC\), as the altitudes meet the sides at

Also, \(\angle A\) is common to both triangles

and \(ABX\).

Here, two corresponding pairs of angles and one

are equal.

Thus by congruence criterion, \(\triangle ACY \cong \triangle ABX\).

Since

and by CPCT, the altitudes \(CY\) and \(BX\) are equal.

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7. Fill up the blanks