Question

in △ghi, (overline{gh}paralleloverline{jk}). given that (ig = 16), (ij = 6), and (ih = 40), find (ik). (ik=square)

Explanation:

Step1: Use the similarity - triangle property

Since $\overline{GH}\parallel\overline{JK}$, then $\triangle IGH\sim\triangle IJK$ by the AA (angle - angle) similarity criterion. The ratios of corresponding sides of similar triangles are equal. That is, $\frac{IG}{IJ}=\frac{IH}{IK}$.

Step2: Substitute the given values

We are given that $IG = 16$, $IJ=6$, and $IH = 40$. Substituting these values into the proportion $\frac{IG}{IJ}=\frac{IH}{IK}$, we get $\frac{16}{6}=\frac{40}{IK}$.

Step3: Cross - multiply and solve for $IK$

Cross - multiplying gives us $16\times IK=6\times40$. So, $16IK = 240$. Then, $IK=\frac{240}{16}=15$.

Answer:

$15$