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If Two Angles of a Triangle Are Unequal Then the Side Opposite to the Greater Angle Is Greater Than the Side Opposite to Smaller Angle

In the figure...

Question

In the figure below, ABC is a right angled triangle. AB = 10 centimetres and AC = 6 centimetres. The midpoint of AB is M.

Compute the lengths of the sides of ΔMBN.

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Solution

Given: AB = 10 cm, AC = 6 cm

Also, M is the midpoint of AB.

Applying Pythagoras theorem in ΔABC:

Since ∠MNB = ∠ACB = 90°, MN || AC by converse of corresponding angles axiom.

We know that in a triangle, a line through the midpoint of a side and parallel to another side bisects the third side.

As M is the midpoint of AB and MN || AC, BN = NC.

Also, (As M is the midpoint of AB)

Applying Pythagoras theorem in ΔBNM:

Thus, the lengths of the sides of ΔBNM are BM = 5 cm, BN = 4 cm, and MN = 3 cm.

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In the figure below, ABC is a right angled triangle. AB = 10 centimetres and AC = 6 centimetres. The midpoint of AB is M. Compute the lengths of the sides of ΔMBN.

In the figure below, ABC is a right angled triangle. AB = 10 centimetres and AC = 6 centimetres. The midpoint of AB is M.

Compute the lengths of the sides of ΔMBN.