R. D. Sharma Solutions for Chapter: Geometrical Constructions, Exercise 2: EXERCISE

How many lines can be drawn which are perpendicular to a given line and pass through a given point lying on it?

Draw a line $PQ$. Take a point $R$ on it. Draw a line perpendicular to $PQ$ and passing through $R$. Using ruler and compasses.

Draw a line $l$. Take a point $A$, not lying on $l.$ Draw a line m such that $m$ is perpendicular to $l$ and passing through $A$. Using ruler and compasses.

Draw a line $AB$ and take two points $C$ and $E$ on opposite sides of $AB$. Through $C$, draw $CD \perp AB$ and through $E$ draw $EF \perp AB$. Using ruler and compass

Using a protractor, draw $\angle BAC$ of measure $70°$. On side $AC,$ take a point $P$, such that $AP = 2 cm$. From $P$ draw a line perpendicular to $AB$.

Draw a line segment $AB$ of length $8 \mathrm{cm}$. At each end of this line segment, draw a line perpendicular to $AB$. Are these two lines parallel?

Using a protractor, draw $\angle BAC$ of measure $45°$. Take a point $P$ in the interior of $\angle BAC$. From $P$ draw line segments $PM$ and $PN$ such that $PM \perp AB$ and $PN \perp AC$, Measure $\angle MPN$.

Draw an angle and label it as $\angle BAC$. Draw its bisector ray $AX$ and take a point $P$ on it. From $P$ draw line segments $PM$ and $PN$, such that $PM \perp AB$ and $PN \perp AC$, where $M$ and $N$ are respectively points on rays $AB$ and $AC$. Measure $PM$ and $PN$. Are the two lengths equal?