In the adjoining figure, points X, Y, Z are the midpoints of of ∆ABC

1.	In the adjoining figure, points X, Y, Z are the midpoints of of ∆ABC respectively, cm. Find the lengths of side AB, side BC and side AC AB = 5 cm, AC = 9 cm and BC = 11c.m. Find the lengths of XY, YZ, XZ.
Answer» i. AC = 9 cm [Given] Points X and Y are the midpoints of sides AB and BC respectively. [Given] ∴ XY = 1/2 AC [Midpoint theorem] = 1/2 x 9 = 4.5 cm ii. AB = 5 cm [Given] Points Y and Z are the midpoints of sides BC and AC respectively. [Given] ∴ YZ = 1/2 AB [Midpoint theorem] =1/2 x 5 = 2.5 cm iii. BC = 11 cm [Given] Points X and Z are the midpoints of sides AB and AC respectively. [Given] ∴ XZ = 1/2 BC [Midpoint theorem] = 1/2 x 11 = 5.5 cm l(XY) = 4.5 cm, l(YZ) = 2.5 cm, l(XZ) = 5.5 cm

In the adjoining figure, points X, Y, Z are the midpoints of of ∆ABC respectively, cm. Find the lengths of side AB, side BC and side AC AB = 5 cm, AC = 9 cm and BC = 11c.m. Find the lengths of XY, YZ, XZ.

Answer»

i. AC = 9 cm [Given]

Points X and Y are the midpoints of sides AB and BC respectively. [Given]

∴ XY = 1/2 AC [Midpoint theorem]

= 1/2 x 9 = 4.5 cm

ii. AB = 5 cm [Given]

Points Y and Z are the midpoints of sides BC and AC respectively. [Given]

∴ YZ = 1/2 AB [Midpoint theorem]

=1/2 x 5 = 2.5 cm

iii. BC = 11 cm [Given]

Points X and Z are the midpoints of sides AB and AC respectively. [Given]

∴ XZ = 1/2 BC [Midpoint theorem]

= 1/2 x 11 = 5.5 cm

l(XY) = 4.5 cm, l(YZ) = 2.5 cm, l(XZ) = 5.5 cm

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