Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to ∆ ABC in which PQ = 8 cm. Also justify the construction
Solution:
Steps of Construction
1. Construct a line segment BC = 5 cm
2. Draw OQ which is the perpendicular bisector of line segment BC meeting BC at P’.
3. Consider B and C as centres construct two arcs of equal radius 6 cm which intersects each other at the point A
4. Now join BA and CA. ∆ABC is the required triangle.
5. From the point B, construct any ray BX which makes an acute angle ∠CBX
6. Let us locate four points B1, B2, B3 and B4 where BB1 = B1B2 = B2B3 = B3B4
7. Join B3C and from the point B4 construct a line B4R||B3C which intersects the extended line
8. From the point R, construct RP||CA which meets BA produced at P
∆ PBR is the required triangle.
Justification:
Consider BB1 = B1B2 = B2B3 = B3B4 = x
From the construction
B4R||B3C
BC/CR = BB3/B3B4 = 3x/x = 3
BC/CR = 3/1
Here
BR/BC = (BC + CR)/BC = BC/BC + CR/BC
= 1 + 1/3
= 4/3
From construction, RP||CA
So rABC is congruent to rPBR [by AAA criterion]
PB/AB = RP/CA = 4/3
The new triangle PBR is similar to isosceles triangle ABC and its sides are 4/3 times of the corresponding sides of ABC.
Therefore, a triangle PQR similar to triangle ABC is drawn.
✦ Try This: Draw an isosceles triangle ABC in which AB = AC = 3 cm and BC = 4 cm. Construct a triangle PQR similar to ∆ ABC in which PQ = 6cm. Also justify the construction.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11
NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 4
Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to ∆ ABC in which PQ = 8 cm. Also justify the construction
Summary:
An isosceles triangle ABC with AB = AC = 6 cm and BC = 5 cm is drawn. A triangle PQR similar to ∆ ABC in which PQ = 8 cm is constructed
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