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\\November 23, 2023 10:09 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

on the Basis of angles A

Acute-angled triangle: A triangle is called an acute-angled triangle, if 56°
all its angles are less than 90°, i.e., acute angles.

In the adjoining figure, DABC is an acute-angled triangle as ∠A, ∠B 67° 57°
and ∠C all are less than 90°. B C
Obtuse-angled triangle: A triangle is called an obtuse-angled triangle, A
if it has one obtuse angle, i.e., greater than 90°.

In the adjoining figure, DABC is an obtuse-angled triangle, as 105°
∠ABC = 105°, i.e., obtuse angle. B C
right-angled triangle: A triangle is called a right-angled triangle, if it has one right angle,
i.e., 90°. P

In the adjoining figure, DPQR is a right-angled triangle, as ∠PQR = 90°. Hypotenuse

properties of a triangle Q 90° R

1. The sum of all three angles of a triangle is 180°. A
In DABC, that is, given alongside, ∠A = 60°, ∠B = 50°, ∠C = 70° 60°

So, ∠A + ∠B + ∠C = 60° + 50° + 70° = 180°
2. The sum of measures of any two sides of a triangle is always greater B 50° 70° C
than the measure of the third side. P
In DPQR given alongside, PQ = 2 cm, QR = 4 cm and PR = 3 cm.

Now, PQ + QR = 2 cm + 4 cm = 6 cm and PR = 3 cm 2 cm 3 cm
Clearly, PQ + QR > PR
Check for the same other combinations of sides. Q 4 cm R

Think and Answer

Answer the following:
1. How many acute angles can a triangle have? 2. How many right angles can a triangle have?
3. How many obtuse angles can a triangle have?

practice time 6e

1. Choose the correct option:
(a) A triangle has __________ parts.

(i) 2 (ii) 4 (iii) 6 (iv) 3
(b) The right-angled triangle can have _________ right angle(s).
(i) 0 (ii) 1 (iii) 2 (iv) 3
(c) The maximum number of acute angles a triangle can have is _________.

(i) 0 (ii) 1 (iii) 2 (iv) 3

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