Telangana SCERT Class 6 Maths Chapter 13 Solution – Practical Geometry. Here in this post we provides Class 6 Maths Practical Geometry Telangana State Board Solution. Telangana State Board English Class VI Medium Students can download this Solution to Solve out Improve Your Learning Questions and Answers.
Telangana State Board Class 6 Maths Chapter 13 Practical Geometry Solution:
EXERCISE – 13.1
1.) Construct a line segment of length 6.9 cm using ruler and compasses.
ANSWER:
We have to construct line segment of length 6.9 cm using ruler and compasses.
Steps to draw line segment of length 6.9 cm using ruler:
1st we place ruler on paper. We marking a point with a sharpened pencil against 0 cm mark of the ruler. Name the point as A. we Mark another point against 9 small divisions just after the 6 cm mark. Name this point as B. Join points A and B along the edge of the ruler. AB is the required line segment of length 6.9 cm
Steps to draw line segment of length 6.9 cm using compass:
Step-1: We draw a line l. Mark a point A on the line l.
Step-2: Place the metal pointer of the compasses on the zero mark of the ruler. Open the compasses so that pencil point touches the 6.9 cm mark on the ruler.
Step-3: Place the pointer on A on the line l and draw an arc to cut the line. Mark the point where the arc cuts the line as B.
Step-4: On the line l, we got the line segment AB of required length.
2.) Construct a line segment of length 4.3 cm using ruler.
ANSWER:
We have to construct a line segment of length 4.3 cm using ruler.
Steps to draw line segment of length 4.3 cm using ruler:
1st we place ruler on paper. We marking a point with a sharpened pencil against 0 cm mark of the ruler. Name the point as A. we Mark another point against 3 small divisions just after the 4 cm mark. Name this point as B. Join points A and B along the edge of the ruler. AB is the required line segment of length 4.3 cm
3.) Construct a line segment MN of length 6cm. Mark any point O on it. Measure MO, ON and MN. What do you observe?
ANSWER:
Here, we have to construct a line segment MN of length 6cm.
We have to Measure MO, ON and MN.
When we measure MO and ON with ruler
MO = ON = 3 cm
4.) Draw a line segment AB of length 12 cm Mark a point C on the line segment AB, such that AC = 5.6 cm. What should be the length of CB? Measure the length of CB.
ANSWER:
Here, we have to draw line segment AB of length 12 cm.
Marking a point C on the line segment AB, such that AC = 5.6 cm.
We have to find what should be the length of CB.
Line segment AB = 12 cm
Line segment AC = 5.6 cm
Line segment CB =?
Line segment CB = Line segment AB – Line segment AC
Line segment CB = 12 – 5.6
Line segment CB = 6.4 cm
5.) Given that AB = 12 cm
ANSWER:
(i) From the above figure measure the lengths of the following line segments.
(a) CD
ANSWER:
Given, AB = 12 cm
By measuring the lengths of the line segments by ruler
Length of line segment CD = 15 cm
(b) DB
ANSWER:
Given, AB = 12 cm
By measuring the lengths of the line segments by ruler
Length of line segment DB = DC + CB
Length of line segment DB = 15 cm + 8 cm
Length of line segment DB = 23 cm.
(c) EA
ANSWER:
Given, AB = 12 cm
By measuring the lengths of the line segments by ruler
Length of line segment EA = AB + BC + CD + DE
Length of line segment EA = 12 + 8 + 15 + 5
Length of line segment EA = 40 cm
(d) AD
ANSWER:
Given, AB = 12 cm
By measuring the lengths of the line segments by ruler
Length of line segment AD = AB + BC + CD
Length of line segment AD = 12 + 8 + 15
Length of line segment AD = 35 cm
(ii) Verify AE – CE = AC?
ANSWER:
We have to verify AE – CE = AC
By measuring distance with ruler,
AE = 40 cm
CE = 20 cm
AC = 20 cm
AE – CE = AC
40 – 20 = 20
Hence, AE – CE = AC verify.
6.) AB = 3.8 cm. Construct MN by compasses such that the length of MN is thrice that of AB.Verify this with the help of a ruler.
ANSWER:
Given, AB = 3.8 cm.
We have to construct MN by compasses such that the length of MN is thrice that of AB.
MN = 3 x AB.
MN = 3 x 3.8
MN = 11.4 cm
Steps to draw line segment of length 11.4 cm using compass:
Step-1: We draw a line l. Mark a point A on the line l.
Step-2: Place the metal pointer of the compasses on the zero mark of the ruler. Open the compasses so that pencil point touches the 11.4 cm mark on the ruler.
Step-3: Place the pointer on A on the line l and draw an arc to cut the line. Mark the point where the arc cuts the line as B.
Step-4: On the line l, we got the line segment AB of required length.
EXERCISE – 13.2
1.) Construct a circle with centre M and radius 4 cm
ANSWER:
Here we have to construct a circle with centre M and radius 4 cm.
Steps to draw a circle with centre M and radius 4 cm:
Step-1: Open the compasses for required radius of 4 cm
Step-2: Mark a point with sharp pencil. This is the centre. Mark it as M.
Step-3: Place the pointer of the compasses firmly at M.
Step-4: Without moving its metal point.Slowly rotate the pencil till it comes back to the starting point.
2.) Construct a circle with centre X and diameter 10 cm
ANSWER:
Here we have to construct a circle with centre X and diameter 10 cm.
We know,
Radius of circle = Diameter / 2
Radius of circle = 10 cm / 2
Radius of circle = 5 cm
We have to construct a circle with centre X and radius 5 cm.
Steps to draw a circle with centre X and radius 5 cm:
Step-1: Open the compasses for required radius of 5 cm
Step-2: Mark a point with sharp pencil. This is the centre. Mark it as X.
Step-3: Place the pointer of the compasses firmly at X.
Step-4: Without moving its metal point. Slowly rotate the pencil till it comes back to the starting point.
3.) Draw four circles of radii 2cm, 3cm, 4cm and 5cm with the same centre P.
ANSWER:
Here, we have to draw circles of radii 2cm, 3cm, 4cm and 5cm with the same centre P
4.) Draw any circle and mark three points A, Band C such that
(i) A is on the circle
(ii) B is in the interior of the circle
(iii) C is in the exterior of the circle.
ANSWER:
Here, we have to draw circle, marking three points A, Band C such that
(i) A is on the circle
(ii) B is in the interior of the circle
(iii) C is in the exterior of the circle.
EXERCISE – 13.3
1.) Draw a line segment PQ = 5.8cm and construct its perpendicular bisector using ruler and compasses.
ANSWER:
Here, we have to draw line segment PQ = 5.8cm and construct its perpendicular bisector using ruler and compasses.
Steps to draw perpendicular bisector using ruler and compasses:
Step-1: Draw a line segment PQ = 5.8cm.
Step-2: Set the compasses as radius more than half of the length of PQ.
Step-3: With P as centre, draw arcs below and above the line segment.
Step-4: With the same radius and Q as centre draw two arcs above and below the line segment to cut the previous arcs. Name the intersecting points of arcs as M and N.
Step-5: Join the points M and N. Then, the line l is the required perpendicular bisector of the line PQ. Line l intersects line PQ at O.
2.) Ravi made a line segment of length 8.6 cm. He constructed a bisector of AB on C. Find the length of AC & BC.
ANSWER:
Given, Ravi made a line segment of length 8.6 cm.
He constructed a bisector of AB on C.
We have to find the length of AC & BC.
We know,
When we draw bisector of any line, the line is divided in two equal parts.
AB = AC + CB
8.6 cm = AC + CB
But AC and CB are equal.
AC = CB = 8.6 / 2
AC = CB = 4.3 cm
3.) Using ruler and compasses, draw AB = 6.4 cm. Find its mid-point.
ANSWER:
We have to draw AB = 6.4 cm using ruler and compasses.
We have to find its mid-point.
Point p is mid-point of line AB.
AP = PB = 6.4 /2
AP = PB = 3.2 cm
EXERCISE – 13.4
1.) Draw the following angles with the help of a protractor.
(i) ∠ABC = 65°
ANSWER:
We have to draw angles with the help of a protractor
∠ABC = 65°
Step-1: Draw a ray BC of any length.
Step-2: Place the centre point of the protractor at Band the line aligned with the BC
Step-3: Mark a point A at 65°.
Step-4: Join BA.
Then∠ABC is the required angle
(ii) ∠PQR = 136°
ANSWER:
We have to draw angles with the help of a protractor.
Step-1: Draw a ray QR of any length.
Step-2: Place the centre point of the protractor at Q and the line aligned with the QR
Step-3: Mark a point P at 136°.
Step-4: Join QP. Then ∠PQR is the required angle.
(iii) ∠Y= 45°
ANSWER:
We have to draw angles with the help of a protractor.
Step-1: Draw a ray YZ of any length.
Step-2: Place the centre point of the protractor at Y and the line aligned with the YZ
Step-3: Mark a point X at 45°.
Step-4: Join XY. Then ∠XYZ is the required angle.
(iv) ∠O = 172°
ANSWER:
We have to draw angles with the help of a protractor.
Step-1: Draw a ray OB of any length.
Step-2: Place the centre point of the protractor at O and the line aligned with the OB
Step-3: Mark a point A at 172°.
Step-4: Join AO. Then ∠AOB is the required angle.
EXERCISE – 13.5
1.) Construct ∠ABC = 60° without using protractor.
ANSWER:
We have to construct ∠ABC = 60° without using protractor.
2.) Construct an angle of 120° with using protractor and compasses.
ANSWER:
We have to construct an angle of 120° with using protractor and compasses.
Steps to draw an angle of 120° with using protractor and compasses:
Step-1: Draw any ray OA
Step-2: Place the pointer of the compasses at O. With O as centre and anyconvenient radius draw an arc cutting OA at M.
Step-3: With M as centre and without altering radius (as in step 2) draw an arc which cuts the first arc at P.
Step-4: With P as centre and without altering the radius (as in step 2) draw an arc which cuts the first arc at Q.
Step-5: Join OQ. Then ∠AOQ is the required angle
Also See: Chapter No. 12 Symmetry Solution