Draw a line l and a point X on it. Through X , draw a line segment X Y - perpendicular to l . Now draw a perpendicular to X Y - at Y . (use ruler and compasses)

Steps of construction: (i) Draw a line ‘ l ’ and mark a point X on it. (ii) Choose any convenient radius and with the pointed end of the compass at X , draw an arc intersecting the line ‘ l ’ at two points A and B . (iii) With A and B as centers and a radius greater than X A , draw two arcs, which intersect at a point, say C . (iv) Join X C and produce it to Y . Therefore, we obtain X Y perpendicular to ‘ l ’. (v) Choose any convenient radius and with the pointed end of the compass at Y , draw an arc intersecting X Y at two points P and Q . (vi) With P and Q as centers and radius greater than Y P , draw two arcs which intersect each other at a point say Z . (vii) Join Y Z . Therefore, we obtain Y Z perpendicular to X Y at Y .

Draw the perpendicular bisector of X Y - whose length is 10.3 c m . Take any point P on the bisector drawn. Examine whether P X = P Y .

Steps of construction: (i) Draw a line l and mark a point X on it. (ii) Using a compass and ruler, cut an arc of 10 . 3 cm on the line. The point of intersection will be Y. So, we obtain X Y - = 10.3 c m (iii) With X as the center and radius more than half of X Y - , draw arcs above and below the line segment X Y - . (iv) With Y as the center and radius same as in step (iii), draw arcs above and below the line segment X Y - . (v) Name the point of intersection above the line segment as C and the point of intersection below the line segment as D . (vi) Join C and D . (vii) C D is the required perpendicular bisector of X Y - . Now: Take any point P on the bisector drawn. With the help of divider we can check that P X - = P Y - .

EASY

Earn 100

Your geometry box has two set squares. In a given set square angles are

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Important Questions on Practical Geometry

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

The set squares are two triangular pieces, one of the set square has angles of

45 ° - 45 ° -

_____

°

at their vertices.

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a line

l

and a point

X

on it. Through

X,

draw a line segment

\bar{X Y}

perpendicular to

l .

Now draw a perpendicular to

\bar{X Y}

Y .

(use ruler and compasses)

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a circle with centre

C

and radius

3.4 c m .

Draw any chord

AB .

Construct the perpendicular bisector of

AB

and examine if it passes through

C .

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw the perpendicular bisector of a given line segment $A B$ of length

6 cm

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a line $A B$ . Take a point $P$ outside it. Draw a line passing through $P$ and perpendicular to $A B$ .

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw any line segment

\bar{A B} .

Mark any point

M

on it. Through

M,

draw a perpendicular to

\bar{A B} .

(use ruler and compasses)

EASY

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

The number of perpendiculars that can be drawn from a point not on the line are

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw any angle with vertex

O .

Take a point

A

on one of its arms and

B

on another such that

O A = O B .

Draw the perpendicular bisectors of

OA

and

OB .

Let them meet at

P .

P A = P B ?

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Find the distance between the parallel lines $l$ and $m$ , using a set square.

Question Image

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a circle of radius

4 c m

. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a line segment

A B = 6 cm

. Take a point $C$ on $A B$ such that

A C = 2.5 cm

. Draw $C D$ perpendicular to $A B$ .

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a line segment

A B = 5.6 cm

. Draw the right bisector of $A B$ .

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw any line segment

\bar{P Q} .

Take any point

R

not on it. Through

R,

draw a perpendicular to

\bar{P Q} .

(use ruler and set-square)

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Perpendicular to a line from a given point not on it can be obtained by paper folding technique.

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a circle with centre

C

and radius

3.4 c m .

Draw a diameter

AB .

Construct the perpendicular bisector of

AB

and examine if it passes through

C .

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw the perpendicular bisector of

\bar{X Y}

whose length is

10.3 c m .

Take any point

P

on the bisector drawn. Examine whether

P X = P Y .

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

There are two “set-squares” in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

With

PQ

of length

6.1 c m

as diameter, draw a circle.

HARD

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a line segment of length

12.8 c m .

Using compasses, divide it into four equal parts. Verify by actual measurement.

MEDIUM

Mathematics>Geometry>Practical Geometry>Introduction to Practical Geometry

Draw a line $A B$ . Take a point $P$ on it. Draw a line passing through $P$ and perpendicular to $A B$ .

Your geometry box has two set squares. In a given set square angles are

Important Questions on Practical Geometry

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