Ncert -Class 7- maths -worksheet – The Triangle and Its Properties
1. A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
2. A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
3. A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree
4. The diagonals of a rhombus measure 16 cm and 30 cm. find its perimeter
5.Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to
show such a case).
6.Find the unknown value:-
(a) In the triangle ABC, B= 90°, AB = 3cm, BC = 4cm, AC = ?
(b) In the triangle ABC, A= 90°, AB = 6cm , AC = 8cm , BC=?
(c) In the triangle ABC, C= 90°, BC= 12cm, AC = 5cm, BC=?
(d) In the triangle PQR, Q = 90°, PQ= 12cm, PR =13cm , QR=?
(e) In the triangle KLM,L = 90°, KM = 17cm,KL=12cm , LM=?
(f)In the triangle NOW, NO= 40cm, OW= 9cm and NW= 41cm. find the degree measure of O.
7. The hypotenuse of a right-angled triangle is 15 cm long and length of the base is 5 cm. Find the height of the triangle.
8.A 25 m long ladder riches a roof of 20 m high from the ground on placing it against the wall. How far is the foot of the ladder from the wall?
9.One of the acute angles of a right-angled triangle is 50°. Find the other acute angle.
10. Is it possible to have a triangle with the following sides?
3 cm, 5 cm, 7cm
11. If the angles of a triangle are in the ratio 2 : 3 : 4, then find the three angles of the triangle.
12. The hypotenuse of a right triangle is 17 cm long. If one of the remaining two sides is 8 cm in length,
then the length of the other side is:
(a)15 cm
(b) 12 cm
(c) 13 cm
(d) none of these.
13. (ii).Which is the longest side in the triangle ABC right angled at B?
(a) AB
(b) BC
(c) AC
(d) none of these.
14.What do you mean by perimeter in triangle?
- The sum of all the 3 angles of a triangle.
- The sum of all the 3 sides of a triangle.
- The sum of all the sides and angles of a triangle.
- None of them
Ans. Correct option is 2
Perimeter is the sum of all the sides of a triangle.
15. Can we form an exterior angle on every vertex of a triangle?
(a) No (b) Yes (c) Might be (d) None of them
16.Pythagoras property hold only if the triangle is
(a) Right angled triangle
(b) Obtuse angled triangle
(c) Acute angled triangle
(d) None of them
17. Six elements of a triangle are
(a) three points and three angles.
(b) three altitudes and three sides.
(c) three sides and three angles.
(d) three sides and three points.
Ans: (c)
Explanation:
Every triangle has six measurements of a triangle, which are
also called as six elements of a triangle.
18. The line segment joining a vertex to the mid-point of the
opposite side is called as the
(a) hypotenuse of the triangle.
(b) median of the triangle.
(c) perpendicular of the triangle.
(d) altitude of the triangle.
Ans: (b)
19. The line segment drawn perpendicular from the vertex to the opposite side is called as the
(a) hypotenuse of the triangle.
(b) median of the triangle.
(c) perpendicular of the triangle.
(d) altitude of the triangle.
Ans: (d)
Explanation:
An altitude has one end point at a vertex of the triangle and the
other on the line containing the opposite side.
20. If three angles of a triangle are (2x + 20)°, (x + 30)°, and (2x – 10)°, then the angles will be
(a) 52°, 60°, and 58°, respectively.
(b) 76°, 55°, and 49°, respectively.
(c) 76°, 58°, and 46° respectively.
(d) 80°, 61°, and 47°, respectively.
Ans: (c)
Explanation:
By angle sum property of a triangle,
(2x + 20) + (x + 30) + (2x – 10) = 180
x = 28
Therefore, required angles = 76°, 58°, and 46°