Class 8 Exam  >  Class 8 Notes  >  NCERT Solutions (Ex - 4.4, 4.5) - Practical Geometry, Maths, Class 8

NCERT Solutions (Ex - 4.4, 4.5) - Practical Geometry, Maths, Class 8 PDF Download

Exercise 4.4

Question 1: Construct the following quadrilaterals:

(i) Quadrilateral DEAR

DE = 4 cm, EA = 5 cm, AR = 4.5 cm, ∠E = 60o ,∠A = 90o

(ii) Quadrilateral TRUE

TR = 3.5 cm, RU = 3 cm, UE = 4 cm, ∠ R= 75°, ∠ U = 120°

Answer 1:

(i) Given: DE = 4cm, EA = 5cm, AR = 4.5 cm,  ∠E = 60% ,∠A = 90o

To construct:

A quadrilateral DEAR. Steps of construction:

(a) Draw a line segment DE = 4 cm.

(b) At point E, construct an angle of 60o.

(c) Taking radius 5 cm, draw an arc from point E which intersects at A.

(d) Construct CBSE, NCERT, Syllabus, Important, Class VI, Mathematics, Questions and Answers, Solved , draw an arc of radius 4.5 cm with centre A which intersect at R.

(e) Join RD.

It is the required quadrilateral DEAR.

CBSE, NCERT, Syllabus, Important, Class VI, Mathematics, Questions and Answers, Solved

(ii) Given: TR = 3.5 cm, RU = 3 cm, UE = 4 cm, ∠R = 75°, ∠U = 120o

To construct: A quadrilateral TRUE

Steps of construction:

  1. Draw a line segment TR = 3.5 cm.
  2. Construct an angle 75o at R and draw an arc of radius 3 cm with R as centre, which intersects at U.
  3. Construct an angle of 120° at U and produce the side UE.
  4. Draw an arc of radius 4 cm with U as centre.
  5. Join UE and TE.

It is the required quadrilateral TRUE.

NCERT Solutions (Ex - 4.4, 4.5) - Practical Geometry, Maths, Class 8

 

Exercise 4.5

Question 1:

Draw the following: The square READ with RE = 5.1 cm.

Answer 1:

Given: RE = 5.1 cm.

To construct: A square READ.

Steps of construction:

(i) Draw RE = 5.1 cm.

(ii) At point E, construct an angle of 90o and draw an arc of radius 5.1 cm, which intersects at point A.

(iii) At point R, draw an arc of radius 5.1 cm at point A, draw another arc of radius 5.1 cm which intersects the first arc at point D.

(iv) Join AD and RD.

It is the required square READ,

CBSE, NCERT, Syllabus, Important, Class VI, Mathematics, Questions and Answers, Solved

Question 2:

Draw the following: A rhombus whose diagonals are 5.2 cm and 6.4 cm.

Answer 2:

Given: Diagonals of a rhombus AC = 5.2 cm and BD = 6.4 cm.

To construct: A rhombus ABCD.

Steps of construction:

(a) Draw AC = 5.2 cm and draw perpendicular bisectors on AC.

(b) Since, diagonals bisect at mid-point O, therefore get half of 6.4 cm, i.e., 3.2 cm.

(c) Draw two arcs on both sides of AC of radius 3.2 cm from intersection point O, which intersects at B and D.

(d) Join AB, BC, CD and DA.

It is required rhombus ABCD.

CBSE, NCERT, Syllabus, Important, Class VI, Mathematics, Questions and Answers, Solved

 

Question 3:

Draw the following: A rectangle with adjacent sides of length 5 cm and 4 cm.

Answer 3:

Given: MN = 5 cm and MP = 4 cm.

To construct: A rectangle MNOP

Steps of construction:

(a) Draw a segment MN = 5 cm.

(b) At points M and N, draw perpendiculars of lengths 4 cm and produce them.

(c) Taking centres M and N, draw two arcs of 4 cm each, which intersect P and Q respectively.

(d) Join side PO.

It is required rectangle MNOP.

CBSE, NCERT, Syllabus, Important, Class VI, Mathematics, Questions and Answers, Solved

Question 4:

Draw the following: A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm.

Answer 4:

Given: OK = 5.5 cm and KA = 4.2 cm.

To construct: A parallelogram OKAY.

Steps of construction:

(a) Draw a line segment OK = 5.5 cm.

(b) Draw an angle of 90 at K and draw an arc of radius KA = 4.2 cm, which intersects at point A.

(c) Draw another arc of radius AY = 5.5 cm and at point O, draw another arc of radius 4.2 cm which intersect at Y.

(d) Join AY and OY.

It is the required parallelogram OKAY.

CBSE, NCERT, Syllabus, Important, Class VI, Mathematics, Questions and Answers, Solved

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FAQs on NCERT Solutions (Ex - 4.4, 4.5) - Practical Geometry, Maths, Class 8

1. What is practical geometry?
Ans. Practical geometry is the branch of mathematics that deals with the construction and measurement of geometric figures using a compass, ruler, and other tools.
2. What are some basic geometric constructions that are taught in Class 8?
Ans. Some of the basic geometric constructions that are taught in Class 8 include construction of perpendicular bisectors, angle bisectors, triangles, and quadrilaterals.
3. How do I construct a perpendicular bisector of a line segment using a compass and ruler?
Ans. To construct a perpendicular bisector of a line segment, follow these steps: - Step 1: Draw a line segment AB using a ruler. - Step 2: Place the compass at point A and draw an arc that intersects AB at a point C. - Step 3: Place the compass at point B and draw an arc that intersects AB at a point D. - Step 4: Draw a straight line passing through points C and D. This line is the perpendicular bisector of AB.
4. How do I construct an angle bisector using a compass and ruler?
Ans. To construct an angle bisector, follow these steps: - Step 1: Draw an angle ABC using a ruler and a protractor. - Step 2: Place the compass at point A and draw an arc that intersects AB and AC. - Step 3: Without changing the compass width, place the compass at point B and draw an arc that intersects the previous arc. - Step 4: Draw a straight line passing through point A and the point where the two arcs intersect. This line is the angle bisector of angle ABC.
5. How do I construct a triangle when given its three sides?
Ans. To construct a triangle when given its three sides, follow these steps: - Step 1: Draw a line segment of length equal to the first side of the triangle. - Step 2: Using the compass, draw an arc with the same length as the second side of the triangle, with one end of the arc at one end of the line segment drawn in Step 1. - Step 3: Using the compass, draw another arc with the same length as the third side of the triangle, with one end of the arc at the other end of the line segment drawn in Step 1. - Step 4: The intersection of the two arcs is the third vertex of the triangle. Draw the remaining sides to complete the triangle.
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