Question

In triangle abc,ab=8cm,bc=9 cm and ac=10cm.x,y and z are mid-points of ao,bo and co respectively.find the lengths of the sides of triangle xyz.

Answer 1

Solution :-

According to the midpoint theorem, the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

So,

XY = Half of AB

⇒ Half of 8 cm

⇒ 8/2

XY = 4 cm

YZ = Half of BC

⇒ Half of 9 cm

⇒ 9/2

YZ = 4.5 cm

ZX = Half of AC

⇒ Half of 10 cm

⇒ 10/2

ZX = 5 cm

So, XY = 4 cm, YZ = 4.5 cm and ZX = 5 cm

Answer.

Answer 2

Solution :-

According to the midpoint theorem, the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

So,

XY = Half of AB

⇒ Half of 8 cm

⇒ 8/2

XY = 4 cm

YZ = Half of BC

⇒ Half of 9 cm

⇒ 9/2

YZ = 4.5 cm

ZX = Half of AC

⇒ Half of 10 cm

⇒ 10/2

ZX = 5 cm

So, XY = 4 cm, YZ = 4.5 cm and ZX = 5 cm