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Practical Geometry Class 7 Notes Maths

10. Practical Geometry

Construction of Triangles

Practical Geometry Class 7 Notes Maths

The sum of the measures of the three angles .

1) The sum of the measures of the three angles of a triangle is

Practical Geometry Class 7 Notes Maths
2) The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

AB + BC > CA; BC + CA > AB and CA + AB > BC

3) The difference between the lengths of any two sides of a triangle is always less than the length of the third side.

AB - BC < CA; BC - CA < AB and CA - AB < BC

Practical Geometry Class 7 Notes Maths

Page 39

4) The measure of an exterior angle is equal to the sum of the two remote or opposite interior angles.

Practical Geometry Class 7 Notes Maths

Practical Geometry - Construction of Triangles

The properties of triangles are as follows:

To construct a triangle, we should know any one of the following:

Length of the three sides
Two sides and the included angle
Two angles and the included side
Length of the hypotenuse and one side in case of a right-angled triangle.

Construction of Parallel Lines

Practical Geometry Class 7 Notes Maths

Two lines in a plane that never meet each other at any point are said to be parallel to each other.

Page 40

Two lines in a plane that never meet each other at any point are said to be parallel to each other. Any line intersecting a pair of parallel lines is called a transversal.

Practical Geometry Class 7 Notes Maths

Properties of angles formed by parallel lines and transversal:

1. All pairs of alternate interior angles formed by parallel lines and a transversal are equal.
2. All pairs of corresponding angles formed by parallel lines and a transversal are equal.
3. All pairs of alternate exterior angles formed by parallel lines and a transversal are equal.
4. The interior angles formed on the same side of the transversal are supplementary (the sum of their measures is 1800).

Steps to construct parallel lines using the alternate interior angle property:

1. Draw a line, l.
2. Mark point A outside line l.
3. Mark point B on line l.
4. Draw line joining points A and B.
5. Draw an arc with B as the centre, such that it intersects lines l and n at points D and E, respectively.
6. Draw another arc with the same radius and A as the centre, such that it intersects line n at F.
7. Ensure that the arc drawn from A cuts line n between A and B.
8. Measure distance DE with the help of the compass.
9. Draw another arc with F as the centre and radius equal to DE.
10. Mark the point of intersection of this arc and the previous arc as G.
11. Draw line m passing through A and G.
12. Lines l and m are parallel.

Page 41

Verification of the construction:

If the pair of alternate interior angles ∠ABC and ∠BAG are equal in measure, then line l //line m. Hence, the construction is verified.

Steps to construct parallel lines using the corresponding angle property:

1. Draw line l and point P outside it.
2. Mark point Q on line l.
3. Draw line joining point P and point Q.
4. Draw an arc with Q as the centre, such that it intersects line l at R and line n at S.
5. Draw another arc with the same radius and P as the centre, such that it intersects line n at X.
6. Ensure that the arc drawn from P cuts line n outside QP.
7. Draw another arc withX as the centre and distance RS as the radius, such that it intersects the previous arc at Y.
8. Draw line m passing through points P and Y.
9. Lines l and m are parallel.

Verification of the construction:
If the pair of corresponding angles ∠PQR and ∠XPY are equal in measure, then line l II line m.

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FAQs on Practical Geometry Class 7 Notes Maths

1. What is practical geometry?
Ans. Practical geometry is a branch of mathematics that deals with the construction and measurement of geometric figures using tools such as compasses, rulers, and protractors. It involves solving problems and applying geometric principles to real-world scenarios.
2. What are the basic tools used in practical geometry?
Ans. The basic tools used in practical geometry include a compass, a ruler, and a protractor. The compass is used to draw circles and arcs, the ruler is used for measuring and drawing straight lines, and the protractor is used for measuring angles.
3. How is practical geometry useful in everyday life?
Ans. Practical geometry has various applications in our daily lives. It helps in designing and constructing buildings, bridges, and roads. It is also used in creating maps, blueprints, and diagrams. Additionally, practical geometry is used in carpentry, fashion designing, and various other fields where accurate measurements and shapes are required.
4. What are the different types of angles in practical geometry?
Ans. In practical geometry, there are several types of angles. These include acute angles (less than 90 degrees), obtuse angles (greater than 90 degrees), right angles (exactly 90 degrees), straight angles (exactly 180 degrees), and reflex angles (greater than 180 degrees).
5. How can I improve my skills in practical geometry?
Ans. Improving skills in practical geometry can be done through practice and understanding the principles and concepts involved. It is vital to familiarize yourself with the basic tools and their uses. Additionally, solving a variety of geometry problems and working on construction projects can enhance your skills in practical geometry. Online tutorials, videos, and interactive resources can also be helpful in learning and practicing practical geometry.
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