Question

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same.

Answer 1

Hint:Construct an isosceles triangle ABC using protractor and compass. Find the midpoint of the base and by observing diagram verify whether the median and altitude of an isosceles triangle are the same.

Complete step-by-step answer:
Let us construct an isosceles triangle ABC of base BC = 6cm and equal sides AB = AC = 8cm.
Steps of construction: -
1. Draw a line BC = 6cm.

2. We need to make AB and BC as 8cm. Taking B as center and opening compass to 8cm. We draw an arc. Now, taking C as center, opening the compass to 8 cm, we draw another arc.
3. Where both arcs intersect in point A.
Join AB and AC.
We know BC = 6cm.
\[\therefore \] Midpoint of \[BC=\dfrac{6}{2}=3\]cm
Let’s call the point D.

\[\therefore \] AD is the median of isosceles, \[\vartriangle ABC\].

  

When we measure \[\angle ADC\] by a protractor the angle is \[{{90}^{\circ }}\].
Which means, \[\angle ADC=\angle ADB={{90}^{\circ }}\].
\[\therefore \] AD is perpendicular to BC\[\Rightarrow \]\[AD\bot BC\]
\[\therefore \] AD is the median and altitude of isosceles, \[\vartriangle ABC\].
\[\therefore \] The median of altitude of an isosceles triangle is the same.

Note: By proving \[\angle ADC=\angle ADB={{90}^{\circ }}\], it shows that \[\vartriangle ADB\] and \[\vartriangle ADC\] are right angled triangles and are similar.Thus for the isosceles triangle median and altitude are the same.