Question

Anshu cuts a paper triangle $A B C$ . He folds the paper perpendicular to $B C$ such that it passes through the vertex $A$ . He marks the point where the fold crosses $B C$ as $M$ . He unfolds the paper. He again folds all the three corners such that vertices $A, B$ and $C$ touch $M$ without overlapping.

Radhika performs a similar activity. She marks $M$ by folding $∆ A B C$ such that it halves the side $B C$ . When she folds the three corners such that vertices $A, B$ and $C$ touch $M$ , unlike Anshu, the paper corners overlap.

What can be the reason for overlapping?

Accepted Answer

Given,

An similar activity performed by two different people. Anshu's activity shows no overlapping but Radhika's activity shows overlapping.

We need to find the reason for overlapping.

We know that,

The median of a triangle is the line segment joining a vertex to the mid-point of the other side of a triangle. A triangle contains three medians, one from each vertex.

The altitude of a triangle is perpendicular from a vertex to the opposite side of a triangle is called an altitude. A triangle contains three altitudes, one from each vertex.

In case Anshu's case, he marked the altitude of the side $B C$ , while Radhika marked the median of the side $B C$ .

$A M$ is an altitude from the vertex $A$ to its opposite side $B C$ .

Hence, the required answer is shown above.

Important Questions on The Triangle and its Properties

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