Question

$△XYW$ is a isosceles triangle. Two of its altitudes has a measure of $2.5$ cm. WZ is $2.5$ cm. What is the line XW?

• A. Angle bisector
• B. Median

Answer 1

The correct option is B Median

The given triangle is



Altitudes of $△XYW$ are $XY\&YW$.
Given that altitudes are of same length i.e. $2.5\text{cm}$.

Given that WZ = $2.5\text{cm}$
Hence, W is the mid point of the side YZ.

We know that median is a line from a vertex of a triangle to the midpoint of its opposite side.

$XW$ passes through the vertex of the triangle $△XYZ$ to mid point $W$ of line $YZ$.

$\therefore$ XW is a median of the triangle $△XYZ.$

$XW$ can not be angle bisector because $△XYZ$ is a right-angled triangle with right angle at $\angle XYZ$ so, both other angles of the triangle must be less than ${90}^o$.

As $△XYW$ is an isoscles right triangle, hence, $\angle YXW=\angle XWY={45}^o$ so, $\angle WXZ$ can not be ${45}^o$.