Answer:
The lengths of MN is 22 units, MO is 26 units and JK is 10 units
Step-by-step explanation:
A line segment joining the mid-points of two sides in a triangle is parallel to the third side and equal to half its length
In Δ MON
∵ J, K, and L are mid-points
∵ JL // MN and LK // MO
∴ L is the mid-point of ON
∴ J is the mid-point of MO
∴ K is the mid-point of MN
∵ J, L are the mid-points of MO and ON
∵ JL is opposite to MN
→ By using the rule above
∴ JL = [tex]\frac{1}{2}[/tex] MN
∵ JL = 11 units
∴ 11 = [tex]\frac{1}{2}[/tex] MN
→ Multiply both sides by 2
∴ 22 = MN
∴ MN = 22 units
∵ K, L are the mid-points of MN and ON
∵ KL is opposite to MO
→ By using the rule above
∴ KL = [tex]\frac{1}{2}[/tex] MO
∵ KL = 13 units
∴ 13 = [tex]\frac{1}{2}[/tex] MO
→ Multiply both sides by 2
∴ 26 = MO
∴ MO = 26 units
∵ J, K are the mid-points of MO and MN
∵ JK is opposite to ON
→ By using the rule above
∴ JK = [tex]\frac{1}{2}[/tex] ON
∵ ON =20 units
∴ JK = [tex]\frac{1}{2}[/tex] (20)
∴ JK = 10 units
∴ The lengths of MN are 22 units, MO is 26 units and JK is 10 units
