Draw A B ¯ having length 6 cm and construct its perpendicular bisector P Q ¯ cutting A B ¯ at point M . Measure A M ¯

A line segment is part of a line. It has two end points and its length is fixed. Steps for drawing a line segment using a ruler: 1 . Place the ruler on a paper and hold it firmly. 2 . Mark with pencil two points A & B on paper against the 0 mark and 6 cm mark of the ruler. 3 . Join points A & B by moving the pencil along the ruler. A B is the required line segment of length 6 cm. Steps for drawing perpendicular bisector of a line segment. 1 . With A as centre and radius more than 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 P & Q . 3 . Join points P & Q . Line segment P Q that bisects A B at M is the required perpendicular at bisector of A B . P Q divides the line segment A B is 2 halves. ∴ A M = 1 2 A B = 1 2 × 6 = 3 cm.

Draw A B ¯ having length 6 cm and construct its perpendicular bisector P Q ¯ cutting A B ¯ at point M . Measure M B ¯

A line segment is part of a line. It has two end points and its length is fixed. Steps for drawing a line segment using a ruler: 1 . Place the ruler on a paper and hold it firmly. 2 . Mark with pencil two points A & B on paper against the 0 mark and 6 cm mark of the ruler. 3 . Join points A & B by moving the pencil along the ruler. A B is the required line segment of length 6 cm. Steps for drawing perpendicular bisector of a line segment. 1 . With A as centre and radius more than 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 P & Q . 3 . Join points P & Q . Line segment P Q that bisects A B at M is the required perpendicular at bisector of A B . P Q divides the line segment A B is 2 halves. ∴ M B = 1 2 A B = 1 2 × 6 = 3 cm.

Draw A B ¯ having length 6 cm and construct its perpendicular bisector P Q ¯ cutting A B ¯ at point M . Measure ∠ A M P

A line segment is part of a line. It has two end points and its length is fixed. Steps for drawing a line segment using a ruler: 1 . Place the ruler on a paper and hold it firmly. 2 . Mark with pencil two points A & B on paper against the 0 mark and 6 cm mark of the ruler. 3 . Join points A & B by moving the pencil along the ruler. A B is the required line segment of length 6 cm. Steps for drawing perpendicular bisector of a line segment. 1 . With A as centre and radius more than 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 P & Q . 3 . Join points P & Q . Line segment P Q that bisects A B at M is the required perpendicular at bisector of A B . Since P Q is perpendicular bisector of A B , ∴ ∠ A M P = 90 ∘ cm.

Draw A B ¯ having length 6 cm and construct its perpendicular bisector P Q ¯ cutting A B ¯ at point M . Measure ∠ B M P

A line segment is part of a line. It has two end points and its length is fixed. Steps for drawing a line segment using a ruler: 1 . Place the ruler on a paper and hold it firmly. 2 . Mark with pencil two points A & B on paper against the 0 mark and 6 cm mark of the ruler. 3 . Join points A & B by moving the pencil along the ruler. A B is the required line segment of length 6 cm. Steps for drawing perpendicular bisector of a line segment. 1 . With A as centre and radius more than 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 P & Q . 3 . Join points P & Q . Line segment P Q that bisects A B at M is the required perpendicular at bisector of A B . Since P Q is perpendicular bisector of A B , ∴ ∠ B M P = 90 ∘ cm.

Take any three points A , B and C not lying in a straight path. Join points A and B , B and C . Draw the perpendicular bisectors of A B ¯ and B C ¯ . Let the bisectors meet at point O . With point O as centre and O A ¯ as radius, draw a circle. Does the circle pass through B and C also?

Let A , B , C be three non-collinear points. Join A B & B C . Now steps to draw perpendicular bisectors of A B & B C . 1 . With A as centre and radius more than 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 M is the required perpendicular at bisector of A B . 4 . Again with C as centre and radius more than 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 N is the required perpendicular at bisector of B C . Now let the two perpendicular bisectors meet at a point O . With O as the centre and O A as the radius, if a circle is drawn than this circle will also pass through the points B & C .

E M B I B E

ICSE MATHEMATICS - 6>Geometry>Chapter 15 - Constructions>EXERCISE 15.3

B Nirmala Shastry Solutions for Exercise 3: EXERCISE 15.3

Author:B Nirmala Shastry

B Nirmala Shastry Mathematics Solutions for Exercise - B Nirmala Shastry Solutions for Exercise 3: EXERCISE 15.3

Attempt the practice questions from Exercise 3: EXERCISE 15.3 with hints and solutions to strengthen your understanding. ICSE MATHEMATICS - 6 solutions are prepared by Experienced Embibe Experts.

Questions from B Nirmala Shastry Solutions for Exercise 3: EXERCISE 15.3 with Hints & Solutions

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 1

Draw $\bar{A B}$ having length $6 cm$ and construct its perpendicular bisector $\bar{P Q}$ cutting $\bar{A B}$ at point $M$ . Measure $\bar{A M}$

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 1

Draw $\bar{A B}$ having length $6 cm$ and construct its perpendicular bisector $\bar{P Q}$ cutting $\bar{A B}$ at point $M$ . Measure $\bar{M B}$

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 1

Draw $\bar{A B}$ having length $6 cm$ and construct its perpendicular bisector $\bar{P Q}$ cutting $\bar{A B}$ at point $M$ . Measure $∠ A M P$

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 1

Draw $\bar{A B}$ having length $6 cm$ and construct its perpendicular bisector $\bar{P Q}$ cutting $\bar{A B}$ at point $M$ . Measure $∠ B M P$

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 2

Draw a line segment of length $12 cm$ . Using compass divide it into four equal parts. Verify by measurement.

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 3

Draw a circle with centre $O$ and radius $3.5 cm$ . Draw a chord $P Q$ . Construct the perpendicular bisector of $\bar{P Q}$ and check whether it passes through centre $O$ .

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 4

Take any three points $A, B$ and $C$ not lying in a straight path. Join points $A$ and $B, B$ and $C$ . Draw the perpendicular bisectors of $\bar{A B}$ and $\bar{B C}$ . Let the bisectors meet at point $O$ . With point $O$ as centre and $\bar{O A}$ as radius, draw a circle. Does the circle pass through $B$ and $C$ also?

HARD

6th ICSE

IMPORTANT

ICSE MATHEMATICS - 6>Chapter 15 - Constructions>EXERCISE 15.3>Q 5

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?

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