Worksheet on Triangles
STD 5
1. Take three non - collinear points L, M, N. Join LM, MN and NL. What figure do you get?
Name:
(a)The side opposite to ∠L.
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(b) The angle opposite to side LN.
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(c) The vertex opposite to side MN.
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(d) The side opposite to angle N.
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2. Classify the triangle into acute triangle, obtuse triangle and right triangle with the following angles:
(a) 90°, 45°, 45°
(b) 60°, 60°, 60°
(c) 80°, 60°, 40°
(d) 130°, 40°, 10°
(e) 90°, 35°, 55°
(f) 92°, 38°, 50°
3. Classify the triangle according to sides, that is, equilateral, isosceles and scalene triangles
(a) 6 cm, 3 cm, 5cm.
(b) 6 cm, 6 cm, 6 cm.
(c) 7 cm, 7 cm, 5 cm.
(d) 8 cm, 12 cm, 10 cm.
(e) 3 cm, 4 cm, 5 cm.
(f) 3.5 cm, 3.5 cm, 4.5 cm.
4. Is it possible to have a triangle with the following angles and sides? Give reason in support of your answer.
(a) 110°, 60°, 30°
(b) 70°, 70°, 70°
(c) 80°, 35°, 65°
(d) 7 cm, 3 cm, 4 cm.
(e) 50°, 50°, 90°
(f) 10 cm, 12 cm, 2 cm.
5. If in a triangle LMN:
(a) ∠L = 80°, ∠M = 50°, find ∠N,
(b) ∠M = 60°, ∠N = 60°, find ∠L,
(c) ∠M = 100°, ∠ N = 30°, find ∠ L,
(d) ∠N = 90°, ∠L = 45°, find ∠M.
Mention the kind of triangle also in each case.
6. The angle of a triangle is in the ratio of 2: 3: 4. Find the measure of each angle of the triangle.
7. One of the two equal angles of an isosceles triangle measures 55°. Determine the other angles.
8. Each side of a ∆ is one third of 3 cm. What kind of triangle is this?
9. One of the acute angles of a right triangle is 48°. Find the other acute angle.
10. Say whether the following statements are true or false:
(a) All the angles of an isosceles triangle are equal.
(b) If one angle of a triangle is obtuse, the other two angles must be acute.
(c) A right triangle can be equilateral.
(d) Equiangular triangle has its three sides also equal.
(e) A triangle can have two obtuse angles.
Answers
Answer:
Q1) A triangle
a) NL
b) ∠L
c) L
d) LM
Q2) a) Right Triangle
b) Acute Triangle
c) Acute Triangle
d) Obtuse Triangle
e) Right Triangle
f) Obtuse Triangle
Q3) a) Scalene Triangle
b) Equilateral Triangle
c) Isoceles Triangle
d) Scalene Triangle
e) Scalene Triangle
f) Isolceles Triangle
Q4) a) No, 110+60+30° is not equal to 180°.
b) No, 70+70+70° is not equal to 180°.
c) Yes. 80+35+65° is equal to 180°.
d) No, 3² + 4² is not equal to 7².
e) No, 50+50+90° is not equal to 180°.
f) No, 2² + 10² is not equal to 12².
Q5) a) ∠N = 180° - (50+70)°
= 180° - 120°
= 60°. (Acute Triangle)
b) ∠L = 180° - (60+60)°
= 180° - 120°
= 60°. (Acute Triangle)
c) ∠L = 180° - (100+30)°
= 180° - 130°
= 50°. (Obtuse Angle)
d) ∠M = 180° - (90+45)°
= 180° - 135°
= 45°. (Right Triangle)
Q6) 2x + 3x + 4x = 180°
9x = 180°
x = 20°
1st angle = 40°
2nd angle = 60°
3rd angle = 80°
Q7) two angles = 55°, 55°
another angle = 180° - (55+55)
= 180° - 110°
= 70°. (ans)
Q8) Equilateral Triangle
Q9) Acute angle = 48°
Right angle = 90°
another angle = 180° - (48+90)
= 180° - 138°
= 42°. (ans)
Q10) a) False
b) True
c) False
d) True
e) False