Practical Geometry Class 7 Notes: Chapter 10

Practical geometry class 7 notes are provided here which can help the class 7 students to learn this chapter in a better and more effective way. These CBSE maths chapter 10 notes are concise and students can not only learn the topics but can also revise the concepts easily. The main topics from this chapter that are included here are-

  • Introduction to practical geometry
  • Constructions using only ruler and compass
  • Construction of triangles with SSS, SAS, ASA, and RHS criterion
  • Example Questions
  • Related Articles

Introduction to Class 7 Practical Geometry

In this chapter, students learn how to construct different shapes i.e. lines and triangles using only a ruler and a compass. For construction of triangles, students learn how to construct triangles when-

  1. Measurement of 3 sides is given (SSS)
  2. Measurement of 2 sides an angle between them is given (SAS)
  3. Measurement of 2 angles and of the side between them is given (ASA)
  4. Length of hypotenuse and the length of one of its sides are given for a right-triangle (RHS)

Construction of Two Parallel Lines Using Ruler and Compass

Steps 1: Draw any line “l” and take a point “A” outside that line. Also, select a point “B” on that line and join point A and point B.

Practical Geometry Class 7 Notes

Step 2: From point B, draw and arc cutting line BA and BL. Mark the “D” and “C” respectively.

Practical Geometry Class 7 Notes

Step 3: From A, draw the arc of same radius from A.

Practical Geometry Class 7 Notes

Step 4: Take the distance CD using the compass and cut the arc FGE at both sides from G.

Practical Geometry Class 7 Notes

Step 5: Draw a straight line which touches both H and A.

Practical Geometry Class 7 Notes

In this, line “m” and line “n” are parallel since angle ABC and angle BAH are alternate interior angles.

Construction of Triangles

SSS: in this, the length of three sides of the triangle are given.

Step 1: To draw a triangle ABC with the given lengths, draw a line BC of the given length using a ruler.

Practical Geometry Class 7 Notes

Step 2: From point B, draw an arc according to the length of BA above the line BC. Then, from point C, draw another arc according to the given length CA.

Practical Geometry Class 7 Notes

Step 3: Name this point as A and join the lines.

Practical Geometry Class 7 Notes

SAS: In this, the measurement of two sides and the angle between them is given. An example is given below for better understanding.

Example:

Construct a triangle PQR with PQ = 3 cm, QR = 5.5 cm and angle PQR = 60 degrees.

Step 1: Draw a QR of length 5.5 cm

Practical Geometry Class 7 Notes

Step 2: From Q, draw QX such that it is making 60 degrees with QR. Then, measure 3 cm from Q on the line QX and mark that point as P. Then by joining P and R, the desired triangle is ready.

Practical Geometry Class 7 Notes

ASA: In this, the degrees of two angles are given and the length of the side between them are given.

Example:

Construct a triangle XYZ with XY = 6 cm, angle ZXY = 30° and angle XYZ = 100°.

Step 1: Draw a line segment XY of length 6 cm.

Practical Geometry Class 7 Notes

Step 2: Draw XP which is making an angle of 30 degrees from XY and YQ which is making an angle of 100 degrees from XY.

Practical Geometry Class 7 Notes

Step 3: Join the lines XP and YQ by converging and mark the point as Z. Triangle XYZ is then constructed using the parameters given.

Practical Geometry Class 7 Notes

RHS: In this type, length of one leg and its hypotenuse are given. An example of the construction using this criterion is given below.

Example: Construct a triangle LMN which is right angles at M and the length of LN and MN are 5 cm and 3 cm respectively.

Step 1: Draw MN having the length of 3 cm and from M, draw a line MX which is perpendicular to MN.

Practical Geometry Class 7 Notes

Step 2: From M, draw an arc of 5 cm on MX and name it L. Now, from L, draw a line segment till N. Now, the triangle LMN is constructed using the given criteria.

Practical Geometry Class 7 Notes

Example Questions

  1. Construct a right angled triangle ABC, where angle B = 90°, BC = 8cm and AC = 10 cm.
  2. Construct an isosceles triangle which has two equal sides of lengths 6.5 cm each and have an angle of 110 degrees between them.
  3. Construct a triangle ABC with AB = 4 cm, BC = 3.5 cm and AC = 4 cm. Also, mention the type of triangle it forms?

Related Articles

To get more such maths and science notes for class 7, keep visiting BYJU’S. Also, get various class 7 sample papers, questions papers, and other study materials to prepare for the exams more efficiently.

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