RD Sharma Chapter 17 Class 9 Maths Exercise 17.2 Solutions has been provided here. Primarily, the exercise revolves around constructing a bisector for the provided angle. Moreover, the questions covered fall thoroughly as per the syllabus and norms of the Central Board of Secondary Education.
RD Sharma Chapter 17 Class 9 Maths Exercise 17.2 Solutions is useful for teaching students about the modes of constructing angles through only compass and ruler.
Learn about RD Sharma Chapter 17 (Constructions) Class 9
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Solutions for Class 9 Maths Chapter 17 Construction Exercise 17.2
Important Definition RD Sharma Chapter 17 Class 9 Maths Exercise 17.2 Solutions
We will learn about RD Sharma Chapter 17 Class 9 Maths Exercise 17.2 Solutions based on the following points-
- Construction of the Bisector of an Angle
- Construction of some Standard Angles – 30°, 60°, 90°, 45° and 120°
Students are asked to construct the bisector of an angle, like 30°, 60°, 90°, 45°, and 120°.
Construction of the Bisector of an Angle
Bisection of an angle refers to dividing the angle into two congruent parts, or simply two equal parts, without measuring the angle.
Construction of some Standard Angles
Construction of Standard angles like 30°, 60°, 90°, 45°, and 120° have to be done using a compass and ruler where the angle measurement is given.
Ques 1: Draw an angle and name it as ∠BAC. Construct different angle, equal to ∠BAC.
Solution-
Steps of construction-
- Draw any angle ABC. (Now will create an angle similar to ∠BAC).
- Draw a line section QR.
- Draw an arc that crosses ∠BAC at E and D using A as a center and take any radius.
- With the equal measurements (set in step 2), Draw an arc from point Q.
- With ‘S’ as center and radius equal to DE, draw an arc that crosses the previous arc at T.
- Join Q and T.
Therefore ∠PQR= ∠BAC
Ques- Draw an obtuse angle. Divide it. Measure each of the angles so formed.
Solution-
Steps of construction:
- Draw an obtuse angle. We take ∠ABC = 120°.
- Draw an arc that crosses AB at P and BC at Q, from center B, and take any radius.
- Draw an arc from spot P by setting a radius of more than half of PQ.
- Copy step 3 using Q as a center and cut the previous arc at R.
- Join BR.
Therefore ∠ABR= ∠RBC = 60°
Ques- Utilizing your compass (protractor), draw an angle of 108°. With this given detail of an angle, draw an angle of 54°.
Solution-
Steps of construction:
- Draw ∠ABC = 108°.
- Draw an arc that crosses AB at P and BC at Q from point B. (Take any radius)
- Draw an arc from spot P by setting a radius of more than half of PQ.
- Copy Step 3 using Q as the center and touch the previous arc at R.
- Join BR.
Therefore ∠RBC = 54°
Ques- Utilizing the protractor, draw a right angle. Divide it to make an angle of measure 45°.
Solution- Steps of construction:
- Draw ∠ABC = 90°.
- Draw an arc that crosses AB at P and BC at Q from point B. (Take any radius)
- Draw an arc from spot P by setting a radius of more than half of PQ.
- Copy step 3 using Q as a center and touch the previous arc at R.
- Join RB.
Therefore ∠RBC= 45°
Frequently Asked Questions (FAQs) of RD Sharma Chapter 17 Class 9 Maths Exercise 17.2 Solutions
Ques 1- Why does angle bisector construction work?
Ans- To bisect an angle means that we have to divide the angle into two equal (congruent) parts without measuring the angle. This Euclidean construction works by making two congruent (equal) triangles.
Ques 2- Which tool is used to construct an angle bisector?
Ans- It concerns the construction of the angle equal to one-third of the given arbitrary angle, using only two tools- an unmarked straightedge and a protractor (compass).