Class 7 Mathematics

Chapter 10: Practical Geometry

STAGE 0: Foundation

Practical Geometry helps us draw accurate shapes using instruments like a ruler, compass, and protractor.

In this chapter, we learn how to construct triangles when some measurements are given.

STAGE 1: Instruments Used

• Ruler: To draw straight lines
• Compass: To draw arcs and circles
• Protractor: To measure and draw angles
• Pencil: Sharp and light

STAGE 2: Construction of a Triangle (SSS Rule)

Given: Lengths of three sides of a triangle

Steps:

Step 1: Draw a line segment AB of given length.
Step 2: With A as centre, draw an arc of radius equal to the second side.
Step 3: With B as centre, draw another arc of radius equal to the third side.
Step 4: Let the arcs intersect at point C.
Step 5: Join AC and BC.

✅ Triangle ABC is the required triangle.

STAGE 3: Construction of a Triangle (SAS Rule)

Given: Two sides and the included angle

Steps:

Step 1: Draw a line segment AB of given length.
Step 2: At point A, draw the given angle using a protractor.
Step 3: On the angle arm, mark point C such that AC equals the given side.
Step 4: Join BC.

✅ Triangle ABC is the required triangle.

STAGE 4: Construction of a Triangle (ASA Rule)

Given: Two angles and the included side

Steps:

Step 1: Draw a line segment AB of given length.
Step 2: At point A, construct the first given angle.
Step 3: At point B, construct the second given angle.
Step 4: Let the two angle arms meet at point C.

✅ Triangle ABC is the required triangle.

STAGE 5: Construction of Right-Angled Triangle (RHS Rule)

Given: Hypotenuse and one side

Steps:

Step 1: Draw the hypotenuse AB of given length.
Step 2: At point A, draw a perpendicular line.
Step 3: With A as centre, mark the given side on the perpendicular.
Step 4: Join the point to B.

✅ Required right-angled triangle is obtained.

STAGE 6: Important Points to Remember

• Always use sharp pencil
• Draw arcs lightly
• Measure carefully
• Label points clearly

STAGE 7: Practice Constructions

1. Construct a triangle with sides 4 cm, 5 cm, and 6 cm.
2. Construct a triangle with one side 6 cm and two angles 45° and 60°.
3. Construct a right-angled triangle with hypotenuse 5 cm and one side 3 cm.

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Shaktimatha CBSE Learning
Class 7 Mathematics – Chapter 10: Practical Geometry

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