Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 4 Geometry Intext Questions
Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 4 Geometry Intext Questions
Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 4 Geometry Intext Questions
Answer the following questions:
Question 1.
The sum of the three angles of a triangle is ______
Solution:
1800
Question 2.
The exterior angle of a triangle is equal to the sum of the _______ angles opposite to it.
Solution:
interior
Question 3.
In a triangle, the sum of any two sides is ____ than the third side.
Solution:
greater
Question 4.
The difference between any two sides of a triangle is _______ than the third side.
Solution:
Smaller
Question 5.
Angles opposite to equal sides are ______ and vice-versa.
Solution:
Equal
Question 6.
The angles of a triangle are in the ratio 4 : 5 : 6
(i) Is it an acute, right or obtuse triangle?
(ii) Is it scalene, isosceles or equilateral?
Solution:
(i) Given the angles of a triangle are in the ratio 4 : 5 : 6 Sum of three angles of a
triangle = 180°.
Let the three angles 4x, 5x and 6x
4x + 5x + 6x = 180°
15x = 180° [∵ Vertically opposite angles are equal]
∴ x = 12°
∴ The angles are 4x ⇒ 4 × 12 = 48°
5x ⇒ 5 × 12 = 60°
6x ⇒ 6 × 12 = 72°
∴ The angle of the triangle are 48°, 60°, 72°
∴ It is an acute angles triangle.
(ii) We know that the sides opposite to equal angles are equal.
Here all the three angles are different.
∴ The sides also different.
∴ The triangle is a scalene triangle.
Question 7.
What is ∠A in the triangle ABC?
Solution:
The exterior angle = sum of interior opposite angles.
∴ ∠A + ∠C = 150° in ∆ABC
But ∠C = 40° [∵ Vertically opposite angles are equal]
Question 8.
Can a triangle have two supplementary angles? Why?
Solution:
Sum of three angles of a triangle is 180°.
∴ Sum of any two angles in a triangle will be less than 180°.
∴ A triangle cannot have two supplimentary angles.
Question 9.
________ shapes have the same shapes but different sizes.
Solution:
Similar
Question 10.
shapes are exactly the same in shape and size.
Solution:
Congruent
Exercise 4.1
Try these Page No. 99
Identify the pairs of shapes which are similar and congruent.
Similar shapes:
(i) W and L
(ii) B and J
(iii) A and G
(iv) B and J
(v) B and Y
Congruent shapes:
(i) Z and I
(ii) J and Y
(iii) C and P You can find more.
(iv) B and K
(v) R and S
(vi) I and Z
Try these Page No. 108
Question 1.
Match the following by their congruence
Solution:
1 – (iv)
2 – (iii)
3 – (i)
4 – (ii)
Try this Page No. 108
Question 1.
In the figure, DA = DC and BA = BC. Are the triangles DBA and DBC congruent? Why?
Solution:
Here AD = CD
AB = CB
DB = DB (common)
∆DBA ≅ ∆DBC [∵ By SSS Congruency]
Also RHS rule also bind here to say their congruency.
Exercise 4.3
Try this Page No. 114
Question 1.
Is it possible to construct a quadrilateral PQRS with PQ = 5 cm, QR = 3 cm, RS = 6 cm, PS = 7 cm and PR = 10 cm. If not, why?
Solution:
The lower triangle cannot be constructed as the sum of two sides 5 + 3 = 8 < 10 cm. So this quadrilateral cannot be constructed.
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