Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.
Solution:
Steps of Construction
1. Construct a line segment BC of length 4.8 cm
2. From the point B, point A is at a distance of 3.6 cm
3. Considering B as centre construct an arc of radius 3.6 cm
4. From the point C, point A is at a distance of 3.0 cm
5. Considering C as centre construct an arc of radius 3.0 cm that intersects the previous arc at the point A
6. Now join AB and AC
So triangle ABC is the required triangle.
Here angle B is smallest as the smallest side is AC
To construct angle B, use the steps mentioned below.
1. Considering B as centre, construct an arc which intersects AB and BC at the points D and E
2. Considering D and E as centre construct arcs which intersect at the point P
3. By joining BP, we get the angle bisector of ∠B
Here ∠ABC = 39°,
So we get
∠ABD = ∠DBC = 1/2 × 139° = 19.5°
Therefore, the smallest angle ∠B is bisected and each part is 19.5°.
✦ Try This: Construct a triangle whose sides are 2.6 cm, 2.0 cm and 3.8 cm. Bisect the smallest angle and measure each part.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 11
NCERT Exemplar Class 9 Maths Exercise 11.3 Problem 4
Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.
Summary:
A triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm are constructed. The smallest angle B is bisected and each part is measured as 19.5°
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