In the worksheet on triangle we will solve different types of questions on triangle.
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. ..................................
(b) The angle opposite to side LN. ..................................
(c) The vertex opposite to side MN. ..................................
(d) The side opposite to angle N. ..................................
2. Find the number of triangles in the figure given below:
Answer:
There are 8 triangles (∆HAD; ∆BEF; ∆BHI; ∆AIJ; ∆CFH; ∆FGD; ∆GEJ; ∆ GAC)
3. Write the name of the vertices, sides and angle of the given triangle. Also give the name of the triangle in 3 different ways.
4. Multiple Choice Questions on (MCQ) Triangles:
Tick (✔) the correct option.
(i) The number of parts in a triangle is
(a) 1; (b) 3; (c) 6; (d) 9
(ii) In ∆PQR, PQ = 3x, QR = 4x, PR= 5x and the perimeter of the triangle is 72 cm. The value of x is
(a) 18 cm; (b) 24 cm; (c) 6 cm; (d) 30 cm
(iii) A point O is inside a triangle ABC (shown in figure).
Join the point O to the vertices A, B and C. In how many triangles will the triangle ABC be divided?
(a) 4; (b) 5; (c) 3; (d) 6
Answer:
4. (i) → (c) 6
(ii) → (c) 6 cm
(iii) → (c) 3
5. In the given triangle, name: (i) side opposite to ∠Q (ii) angle opposite to side QR. (iii) side opposite to vertex P. (iv) vertex opposite to side PQ, |
Answer:
5. (i) side opposite to ∠Q is PR.
(ii) angle opposite to side QR is ∠P.
(iii) side opposite to vertex P is QR.
(iv) vertex opposite to side PQ is R.
6. In the adjoining figure, name: (ii) points which lie in the exterior of ∆ABC (iii) points which lie on ∆ABC |
Answer:
6. (i) points which lie in the interior of ∆ABC are F, G and P.
(ii) points which lie in the exterior of ∆ABC are E, H, J and N.
(iii) points which lie on ∆ABC are A, D, B and C.
Worksheet on Triangle
7. In the adjoining figure, name (i) all the triangles (ii) all the angles (iii) the line segments. (iv) triangles which have ∠S as common. |
Answer:
7. (i) all the triangles are ∆PST, ∆PTQ, ∆QTR, ∆RTS, ∆PTR and ∆QTS.
(ii) all the angles are ∠PTS, ∠PTQ, ∠PTR, ∠QTR, ∠QTS, ∠RTS, ∠TPS, ∠TQS, ∠TRS and ∠TSP.
(iii) the line segments are \(\overline{PT}\), \(\overline{TS}\), \(\overline{SP}\), \(\overline{PQ}\), \(\overline{PR}\), \(\overline{QR}\), \(\overline{RS}\), \(\overline{QS}\), \(\overline{QT}\) AND \(\overline{RT}\).
(iv) triangles which have ∠S as common are ∆PST, ∆RTS and ∆QTS.
Answer:
8. Number of triangles in the given figure is 5.
Worksheet on Triangle
9. 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°
10. Identify the type of triangle based on the lengths of the sides.
Answer:
(i) Isosceles Triangle
(ii) Equilateral Triangle
(iii) Scalene Triangle
11. Classify the triangle according to sides, that is, equilateral, isosceles and scalene triangles
(a) 6 cm, 3 cm, 5 cm.
(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.
12. 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.
13. Find the perimeter of a triangle when its sides are:
(a) AB = 7.6 cm, BC = 4.5 cm, CA = 6.3 cm.
(b) PQ = 4.00, QR = 3 cm, RP = 5 cm.
(c) LM = 4.5 cm, MN = 3.6 cm, NL = 6.2 cm.
14. 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.
16. Draw any triangle and name it PQR. Measure its sides and classify the triangle as Isosceles triangle, scalene triangle or equilateral triangle.
17. The angle of a triangle is in the ratio of 2: 3: 4. Find the measure of each angle of the triangle.
18. One of the two equal angles of an isosceles triangle measures 55°. Determine the other angles.
19. The perimeter of a triangle is 24 cm. Two of its sides are 8 cm and 9 cm. Find the length of its third side.
20. Each side of a ∆ is one third of its perimeter. What kind of triangle is this?
21. One of the acute angles of a right triangle is 48°. Find the other acute angle.
22. 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.
23. Fill in the blanks:
(i) A triangle is ……………………… sided polygon.
(ii) A triangle has ……………………… vertices and ……………………… sides.
(iii) A triangle can be classified on the basis of ……………………… and ……………………….
(iv) A triangle with all sides equal is called a ……………………… triangle.
(v) A triangle whose 2 sides are equal is called a ……………………… triangle.
(vi) A triangle with unequal sides is called a ……………………… triangle.
Answer:
(i) three
(ii) three, three
(iii) sides, angles
(iv) equilateral
(v) isosceles
(vi) scalene
Examples of Properties of Triangle
To Construct a Triangle whose Three Sides are given.
To Construct a Triangle when Two of its Sides and the included Angles are given.
To Construct a Triangle when Two of its Angles and the included Side are given.
To Construct a Right Triangle when its Hypotenuse and One Side are given.
Worksheet on Construction of Triangles.
5th Grade Geometry Page
5th Grade Math Problems
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