Question

1. \\(\overline{kl}\\), \\(\overline{hl}\\) and \\(\overline{kh}\\) are the midsegments of triangle jgi. if the length of \\(\overline{kl}\\) is 16 cm, what is the length of \\(\overline{ji}\\)?

Explanation:

Step1: Recall Midsegment Theorem

The Midsegment Theorem states that the midsegment of a triangle is parallel to the third side and half as long as the third side.

Step2: Identify the relationship

In triangle \( JGI \), \( \overline{KL} \) is a midsegment. So, \( \overline{KL} \) is parallel to \( \overline{JI} \) and \( KL=\frac{1}{2}JI \).

Step3: Solve for \( JI \)

Given \( KL = 16\space\text{cm} \), from \( KL=\frac{1}{2}JI \), we can solve for \( JI \) by multiplying both sides by 2. So, \( JI = 2\times KL \).
Substitute \( KL = 16\space\text{cm} \) into the formula: \( JI=2\times16 = 32\space\text{cm} \).

Answer:

The length of \( \overline{JI} \) is \( \boldsymbol{32\space\text{cm}} \).