Question

in the cube shown below, which lines are intersecting? select all that apply. the cube has vertices labeled h, i, j, k, l, m, n, o. the options are: \overleftrightarrow{hi} and \overleftrightarrow{ko}, \overleftrightarrow{hi} and \overleftrightarrow{jk}, \overleftrightarrow{hk} and \overleftrightarrow{no}, \overleftrightarrow{jk} and \overleftrightarrow{jn}

Explanation:

Step1: Define intersecting lines

Intersecting lines share a common point.

Step2: Check HI and KO

HI (top edge) and KO (front-left edge) are skew, no common point.

Step3: Check HI and JK

HI (top edge) and JK (front-top edge) meet at point I, so intersect.

Step4: Check HK and NO

HK (back-top edge) and NO (front-bottom edge) are skew, no common point.

Step5: Check JK and JN

JK (front-top edge) and JN (front-right edge) meet at point J, so intersect.

Answer:

B. HI and JK, D. JK and JN