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Q: 3. What is the method to construct an angle bisector?

Ans. To construct an angle bisector, follow these steps:1. Draw an angle with vertex O and two arms OA and OB.2. With O as the center, draw an arc that intersects OA and OB at two points, say P and Q.3. With P and Q as centers, draw arcs of the same radius that intersect each other at point R.4. Join O and R. The line OR is the angle bisector of angle AOB.

WE KNOW THAT
A triangle has six elements—3 sides and 3 angles. To construct a unique triangle, 3 elements out of six elements are required under a certain combination. A quadrilateral has 8 elements—4 sides and 4 angles. In addition to these elements a quadrilateral has 2 diagonals which play an important role in determining the size and shape of a quadrilateral. Thus a quadrilateral has 10 elements (4 sides, 4 angles and 2 diagonals) or measurements.

CONSTRUCTING A QUADRILATERAL
To construct a unique quadrilateral we need to know 5 measurements (elements).
Note: To construct a unique quadrilateral simply the knowledge of any five elements is not sufficient.
We will need to know a combination of specific 5 elements.

VARIOUS COMBINATIONS OF ELEMENTS FOR CONSTRUCTING A UNIQUE QUADRILATERAL
With the help of the following measurements we can construct quadrilaterals.
(i) Four sides and a diagonal.
(ii) Three sides and two diagonals.
(iii) Four sides and an angle.
(iv) Three sides and two included angles.
(v) Two adjacent sides and three angles.
(vi) Using special properties of a square or a rhombus, etc.

Solved Example:
Question: Suppose the two sides of the triangle are of the same length of 5.5 cm. One of the angles made by this side of the triangle is 80°. Find the other two angles. Construct the triangle.
Solution: Since the two sides of the triangle are of the same length, the angles made by them with the base will always be the same. The angles made by them are of 80° each. By the property of the sum of the interior angles of a triangle, we have
x + 80° + 80° = 180° (let the third angle is of x degrees).
or, x = 180° – 160° = 20°.
The required triangle
Points to Remember - Practical Geometry | NCERT Textbooks & Solutions for Class 8

Question: What is the maximum number of regions into which a chord will divide a circle?
a. 1
b. 2
c. 3
d. 4
Solution: 2. The maximum number of regions into which a chord will divide a circle is 2, as AB is the chord which divides the circle into two regions.
Points to Remember - Practical Geometry | NCERT Textbooks & Solutions for Class 8

Question: Which of the following angle is possible to construct using a compass?
a. 60 °
b. 32 °
c. 51.25 °
d. 40 °
Solution: A. 60 ° angle is possible to construct using a compass.

Question: To construct a line segment of a given length, which of the following pairs of instruments are needed?
a. Ruler and Protractor
b. Ruler and Compass
c. Compass and Divider
d. Protractor and Divider
Solution: B. Ruler and Compass are used to construct a line segment.

Question: If PQ is the perpendicular bisector of AB then PQ divides AB in the ratio:
a. 1: 2
b. 1: 3
c. 2: 3
d. 1: 1
Solution: D. The perpendicular bisector always divides the segment into 2 equal parts.

∴ PQ divides AB in the ratio 1: 1.

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FAQs on Points to Remember - Practical Geometry - NCERT Textbooks & Solutions for Class 8

1. What are the basic concepts of practical geometry in Class 8?

Ans. The basic concepts of practical geometry in Class 8 include understanding lines, angles, triangles, quadrilaterals, and their properties. Students learn to construct various geometrical shapes using a compass, ruler, and protractor.

2. How can I construct a perpendicular bisector of a line segment?

Ans. To construct a perpendicular bisector of a line segment, follow these steps: 1. Draw the given line segment AB. 2. With A as the center, draw an arc that intersects the line segment at two points, say P and Q. 3. With Q as the center, draw another arc of the same radius that intersects the previous arc at R. 4. Join R and P. The line RP is the perpendicular bisector of the line segment AB.

3. What is the method to construct an angle bisector?

Ans. To construct an angle bisector, follow these steps: 1. Draw an angle with vertex O and two arms OA and OB. 2. With O as the center, draw an arc that intersects OA and OB at two points, say P and Q. 3. With P and Q as centers, draw arcs of the same radius that intersect each other at point R. 4. Join O and R. The line OR is the angle bisector of angle AOB.

4. How can I construct a triangle when given its three sides?

Ans. To construct a triangle when given its three sides, follow these steps: 1. Draw a line segment AB, representing one side of the triangle. 2. With A as the center, draw an arc with a radius equal to the length of the second side. 3. With B as the center, draw another arc with a radius equal to the length of the third side. Both arcs should intersect at a point, say C. 4. Join AC and BC. ABC is the required triangle.

5. Can you explain how to construct a parallelogram when given its two adjacent sides and an angle between them?

Ans. To construct a parallelogram when given its two adjacent sides and an angle between them, follow these steps: 1. Draw a line segment AB, representing one side of the parallelogram. 2. With A as the center, draw an arc with a radius equal to the length of the second side. 3. With B as the center, draw another arc with a radius equal to the length of the first side. Both arcs should intersect at a point, say C. 4. Join AC and BC. ABC is the required parallelogram.

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