1. Stating the problem: We have a parallelogram ABCD. 2. Draw diagonal $AC$. 3. Construct a perpendicular line through point $B$ to $AC$. Let this line intersect $CD$ at point $L$. 4. Construct another perpendicular line through point $D$ to $AC$. Let this line intersect $AB$ at point $K$. 5. Our objective is to find points $L$ and $K$ using the perpendiculars to diagonal $AC$ through points $B$ and $D$ respectively. 6. Since $ABCD$ is a parallelogram, opposite sides are parallel and equal in length. 7. The steps to find $L$ and $K$ typically involve coordinate geometry or vector methods: - Assign coordinates or vectors to $A$, $B$, $C$, and $D$. - Write the equation of line $AC$. - For point $B$, find the perpendicular line to $AC$ passing through $B$ and find its intersection $L$ with line $CD$. - For point $D$, find the perpendicular line to $AC$ passing through $D$ and find its intersection $K$ with line $AB$. Without specific coordinates or lengths, this is the geometric description of how to find points $L$ and $K$. Final answer: Points $L$ and $K$ are defined as the intersections found by the perpendiculars from $B$ and $D$ to diagonal $AC$, intersecting sides $CD$ and $AB$ respectively.