Name: Ruler and Compass Constructions
Uploaded: 2019-07-19
Duration: 9 min 30 s

Question

Draw the outline of a

30 ° - 60 ° - 90 °

set square. Name the triangle thus formed as

△ A B C

. Draw the perpendicular bisectors of the three sides of

△ A B C

. Do the perpendicular bisectors meet at a common point?

Accepted Answer

If we draw the outline of a $30 ° - 60 ° - 90 °$ set square then we will get a triangle with angles $30 ° - 60 ° - 90 °$ i.e. a right-angled triangle. Say this triangle is $A B C .$

Hence $△ A B C$ is a right-angled triangle.

Now say, $A C$ is the longest side of the triangle and hence it is the hypotenuse of the triangle.

Steps to draw perpendicular bisectors of the sides $A B & B C :$

$1 .$ With $A$ as centre and radius more than $\frac{1}{2} A B$ , draw arcs above and below $A B$ using compass.

$2 .$ With $B$ as centre and same radius as in step $1,$ draw arcs cutting the previous arcs at two points.

$3 .$ Join the points. The line segment bisecting $A B$ at $N$ is the required perpendicular at bisector of $A B .$

$4 .$ Again with $C$ as centre and radius more than $\frac{1}{2} B C$ , draw arcs above and below $B C$ using compass.

$5 .$ With $B$ as centre and same radius as in step $4,$ draw arcs cutting the previous arcs at two points.

$6 .$ Join the points. The line segment bisecting $B C$ at $M$ is the required perpendicular at bisector of $B C .$

$7 .$ With $A$ as centre and radius more than $\frac{1}{2} A C$ , draw arcs above and below $A C$ using compass.

$8 .$ With $C$ as centre and same radius as in step $1,$ draw arcs cutting the previous arcs at two points.

$9 .$ Join the points. The line segment will bisecting $A C$ at $O$ is the required perpendicular at bisector of $A C .$

We find that the three perpendicular bisectors meet at point $O .$

Draw the outline of a $30 ° - 60 ° - 90 °$ set square. Name the triangle thus formed as $△ A B C$ . Draw the perpendicular bisectors of the three sides of $△ A B C$ . Do the perpendicular bisectors meet at a common point?

Important Questions on Constructions

Learn and Prepare for any exam you want !

Draw the outline of a 30°-60°-90° set square. Name the triangle thus formed as △ABC. Draw the perpendicular bisectors of the three sides of △ABC. Do the perpendicular bisectors meet at a common point?

Important Questions on Constructions

Learn and Prepare for any exam you want !

Draw the outline of a $30 ° - 60 ° - 90 °$ set square. Name the triangle thus formed as $△ A B C$ . Draw the perpendicular bisectors of the three sides of $△ A B C$ . Do the perpendicular bisectors meet at a common point?