Construction Of Triangles
If I draw a triangle, lengths of whose two sides are 5 cm and 4 cm and the measurement of the angle opposite to the side of length 4 cm is 45°, then let’s see what type of triangle I shall get.
It is seen that it is not possible to draw any triangle with these conditions.
- Firstly, 30° arid 45° are drawn and a straight line 6 cm long is drawn.
- Now straight line AX is drawn and from it 6 cm long is cut off.
- On points, A and B of straight line AB, two angles equal to 45° ∠YAB and ∠ZBX are drawn respectively.
- Now on point B equal to 30° is drawn AY straight line on the same side of BZ ZPBZ. PB and AY cut each other at C point
In ΔABC = 6 cm
Read and Learn More WBBSE Solutions For Class 8 Maths
∠CAB = 45 and ∠ACB = 30°
Proof: ∠XBZ = ∠XAY (By construction)
∴ ∠BZ//AY (∵ Corresponding angles)
∴ ∠ZBP = Alternate angle ∠BCA
∵ ∠ZBP = 30°
∴∠BCA = 30°
∴ In ΔABC ∠CAB = 45°, ∠ACB = 30°
and the opposite side of 30° is AB = 6 cm
“Class 8 WBBSE Maths Chapter 21 solutions, Construction of Triangles study material”
Construction Of Triangles Exercise 21.1
Question 1. If I draw a triangle whose 2 sides are 5 cm and 4 cm and the measurement of the angle opposite to the side of length 4 cm is 45°, then let’s see what type of triangle I shall get. It is seen that it isn’t possible to draw any triangle with these conditions.
Solution:
Given
If I draw a triangle whose 2 sides are 5 cm and 4 cm and the measurement of the angle opposite to the side of length 4 cm is 45°
- With the help of scale two 5 cm long straight lines are drawn.
- With the help of a scale, a ray AX is drawn. On the ray off. Taking AX at point A an angle of 45° ∠XAY is drawn.
- From the ray A, X a straight line AB equal to 5 cm is cut off. Taking B as the centre, taking a radius equal to the straight line 4 cm, an arc is drawn which cuts ray AX at point C. B, and C are joined. An ABC is drawn whose AB = 5 cm, ∠BAC = 45° and BC = 4 cm and the angle opposite to the side BC ∠BAC = 45°.
Question 2. But why is it so? Sometimes we are getting one triangle, sometimes two triangles and sometimes no triangle. It is seen that the perpendicular distance from B on the AX line segment is BM = cm = I say.
Solution:
We see that perpendicular distance AX from point B to the straight line
BM = 3.6 cm l = let
a = 5cm
b = 4cm
We see that if b > a then |a 1 | triangle can be drawn.
If l < b < a then 2 triangles can be drawn.
If b = a then 1 triangle can be drawn.
If b < l then no triangle can be drawn.
If b, = l then 1 triangle can be drawn.
“WBBSE Class 8 Maths Chapter 21, Construction of Triangles solved examples”
If a = b, i.e., try to form a triangle whose two sides a = 5 cm, b = 5 cm and the opposite angle to the 5 cm long side is ∠x= 100°
Question 3. Let’s see whether such a triangle can be drawn.
Solution:
straight line AC is drawn and on point A equal to angle 100°, ∠BAC is drawn.
From the AD side, a 5 cm long AB is cut off. Now taking B as the centre 5 cm straight line equal to taking as radius, on a point on AC an arc is drawn then it is seen that cuts at only on one point of AC, A. So it is not possible to draw a triangle.
Question 4. If a < b, i.e., try to form a triangle whose two sides a = 5 cm, b = 4 cm and the opposite angle of 4the cm long side is x = 100°. Let’s see if such a triangle can be drawn.
Solution:
Given
if a < b, i.e., try to form a triangle whose two sides a = 5 cm, b = 4 cm and the opposite angle of 4 cm long side is x = 100°.
A straight line AC is drawn and on point A equal to angle 100°, ∠BAC is drawn. From the AD side, a 5 cm long AB is cut off.
Now taking point B as a centre and taking a radius length equal to a 4 cm straight line AC cut an arc on any point then it is seen that the AC arc doesn’t cut at any point.
So it is not possible to construct a triangle.
Construction Of Triangles Exercise 21.2
Question 1. Let’s draw a triangle whose two sides are 6 cm and 7 cm and the measurement of the angle opposite to the side of length 7 cm is 60°. Let’s write what will be the measurement of the sides to form a triangle.
Solution:
Measurement of the sides to form the triangle
A straight line AX is drawn and on point A equal to angle 60°, ∠DAX is drawn. From side AD, AB is cut equal to 6 cm long. Taking B as the centre and equal to 7 cm long taking as radius point AX is cut at C. B, and C are joined. ABC is the required triangle.
From point B to AC, if the length of the side is more than the length of the perpendicular drawn then two triangles will be formed.
“WBBSE Class 8 Construction of Triangles solutions, Maths Chapter 21”
Question 2. Let’s construct a triangle whose lengths of two sides are 6 cm and 9 cm and the measurement of the angle opposite to the side of length 9 cm is 105°. Let’s write for what length of sides we will not be able to construct two triangles.
Solution:
“Class 8 WBBSE Maths Chapter 21, Construction of Triangles easy explanation”
A straight line AX is drawn and at AX on point A equal to angle 105°, ∠DAX is drawn. From side AD AB is cut equal to 6 cm long. Taking B as centre equal to 9 cm length taking as radius AX is cut at point C. B, and C are joined. ABC is the required triangle.