Question

Construct a parallelogram $ABCD$ in which $AB=6.5$ cm, $AC=3.4$ cm and the altitude $AL$ from $A$ is $2.5$ cm. Draw the altitude from $C$ and measure it.

Answer 1

Steps of construction:
Step 1: Draw $AB=6.5$ cm
Step 2: Draw a perpendicular at point $A$. Name that ray as $AX$. From point $A$, draw an arc of length $2.5$ cm on the ray $AX$ and name that point as $L$.
Step 3: On point $L$, make a perpendicular. Draw a straight line $YZ$ passing through $L$, which is perpendicular to the ray $AX$.
Step 4: Cut an arc of length $3.4$ cm on the line $YZ$ and name it as $C$.
Step 5: From point $C$, cut an arc of length $6.5$ cm on the line $YZ$. Name that point as $D$.
Step 6: Join $BC$ and $AD$.
Therefore, quadrilateral $ABCD$ is a parallelogram.

The altitude from $C$ measures $2.5$ cm in length.