Practical Geometry Class 7 Notes Maths Chapter 10

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CBSE Class 7 Maths Notes Chapter 10 Practical Geometry

Construction of Triangles

1. Properties of triangles

  • The exterior angle of a triangle is equal in measure to the sum of interior opposite angles.
  • The total measure of the three angles of a triangle is 180°.
  • Sum of the lengths of any two sides of a triangle is greater than the length of the third side.
  • In any right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

2. Essential measurements for the construction of a triangle
A triangle can be drawn if any one of the following sets of measurements is given:

  • Three sides: SSS
  • Two sides and the angle between them: SAS
  • Two angles and the side between them: ASA
  • The hypotenuse and a leg in the case of a right-angled triangle: RHS

Construction of a line parallels to a given line, through a point not on the line.

Steps of Construction

Step 1: Take a line ‘l’ and a point ‘A’ outside ‘l’
Practical Geometry Class 7 Notes Maths Chapter 10 1
Step 2: Take any Point B on l and join B to A.
Practical Geometry Class 7 Notes Maths Chapter 10 2
Step 3: With B as centre and a convenient radius, draw an arc cutting l at C and BA at D.
Practical Geometry Class 7 Notes Maths Chapter 10 3
Step 4: Now with A as centre and the same radius as in Step 3 draw an arc EF cutting AB at G.
Practical Geometry Class 7 Notes Maths Chapter 10 4
Step 5: Place the pointed tip of the compasses at C and adjust the opening so that the pencil tip at D.
Practical Geometry Class 7 Notes Maths Chapter 10 5
Step 6: With the same opening as in Step 5 and with G as centre, draw an arc cutting the arc EF at H.
Practical Geometry Class 7 Notes Maths Chapter 10 6
Step 7: Now, join AH to draw a line ‘m’.
Practical Geometry Class 7 Notes Maths Chapter 10 7

Construction of a triangle when the lengths of its three sides are known (SSS Criterion).

Steps of Construction
Step 1: First, we draw a rough sketch with a given measure.
Practical Geometry Class 7 Notes Maths Chapter 10 8
Step 2: Draw a line segment BC of length 6 cm.
Practical Geometry Class 7 Notes Maths Chapter 10 9
Step 3: From B, point A is at a distance of 5 cm. So with B as centre, draw an arc of radius 5 cm.
Practical Geometry Class 7 Notes Maths Chapter 10 10
Step 4: From C, point A is at a distance of 7 cm. So, with C as centre, draw an arc of radius 7 cm.
Practical Geometry Class 7 Notes Maths Chapter 10 11
Step 5: A has to be on both the arcs drawn. So, it is the point of intersection of arc.
Mark the point of intersection of arcs as A. Join AB and AC. ΔABC is now ready.
Practical Geometry Class 7 Notes Maths Chapter 10 12

Constructing a triangle when the lengths of two sides and the measure of the angle between them are known. (SAS Criterion)

Steps of Construction
Step 1: First we draw a rough sketch with given measures.
Practical Geometry Class 7 Notes Maths Chapter 10 13
Step 2: Draw a line segment QR of length 5.5 cm.
Practical Geometry Class 7 Notes Maths Chapter 10 14
Step 3: At Q, draw QX making 60° with QR.
Practical Geometry Class 7 Notes Maths Chapter 10 15
Step 4: With Q as centre, draw an arc of radius 3 cm. It cuts QX at the point E
Practical Geometry Class 7 Notes Maths Chapter 10 16
Step 5: Join PR. ΔPQR is now obtained.
Practical Geometry Class 7 Notes Maths Chapter 10 17

Constructing a triangle when the measures of two of its angles and the length of the side included between them is given (ASA Criterion)

Steps of Construction
Step 1: Before actual construction, we draw a rough sketch with measures marked on it.
Practical Geometry Class 7 Notes Maths Chapter 10 18
Step 2: Draw XY of length 6 cm.
Practical Geometry Class 7 Notes Maths Chapter 10 19
Step 3: At X, draw a ray XP making an angle of 30° with XY. By the given condition Z must be somewhere on the XP.
Practical Geometry Class 7 Notes Maths Chapter 10 20
Step 4: At Y, draw a ray YQ making an angle of 100° with YX. By the given condition, Z must be on the ray YQ also.
Practical Geometry Class 7 Notes Maths Chapter 10 21
Step 5: Z has to lie on both the rays XP and YQ. So, the point of intersection of two rays is Z.
Practical Geometry Class 7 Notes Maths Chapter 10 22
ΔXYZ is now completed.

Constructing a Right-Angled Triangle when the length of one leg and its hypotenuse are given (RHS Criterion).

Steps of Construction
Step 1: Draw a rough sketch and mask the measures. Remember to mark the right angle.
Practical Geometry Class 7 Notes Maths Chapter 10 23
Step 2: Draw MN of length 3 cm.
Practical Geometry Class 7 Notes Maths Chapter 10 24
Step 3: At M, draw MX ⊥ MN.
Practical Geometry Class 7 Notes Maths Chapter 10 25
Step 4: With N as centre, draw an arc of radius 5 cm.
Practical Geometry Class 7 Notes Maths Chapter 10 26
Step 5: L has to be on the perpendicular line MX as well as on the arc drawn with centre N. Therefore, L is the meeting point of these two ΔLMN is now obtained.
Practical Geometry Class 7 Notes Maths Chapter 10 27

Class 7 Maths Notes

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