The Triangle and Its Properties
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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.
Two sides of a triangle are 4 cm and 7 cm. What can be the length of its third side to make the triangle possible?
In the following figure, find the unknown angles a and b, if l||m.
Which of the following cannot be the sides of a triangle?
(i) 4.5 cm, 3.5 cm, 6.4 cm
(ii) 2.5 cm, 3.5 cm, 6.0 cm
(iii) 2.5 cm, 4.2 cm, 8 cm
I have three sides. One of my angle measure 15°. Another has a measure of 60°. What kind of a polygon am I? If I am a triangle, then what kind of triangle am I?
In figure (i) and (ii), Find the values of a, b and c.
In ∆ABC, write the following:
(a) Angle opposite to side BC.
(b) The side opposite to ∠ABC.
(c) Vertex opposite to side AC.
The sides of a triangle are in the ratio 3 : 4 : 5. State whether the triangle is right-angled or not.
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
One of the equal angles of an isosceles triangle is 50°. Find all the angles of this triangle.
In ΔABC, AC = BC and ∠C = 110°. Find ∠A and ∠B.
Classify the following triangle on the bases of sides
The length of the diagonals of a rhombus is 42 cm and 40 cm. Find the perimeter of the rhombus.
AD is the median of a ΔABC, prove that AB + BC + CA > 2AD (HOTS)
In the given figure, find x.
In the given right-angled triangle ABC, ∠B = 90°. Find the value of x.
In the given figure, name the median and the altitude. Here E is the midpoint of BC.
Find whether the following triplets are Pythagorean or not?
(a) (5, 8, 17)
(b) (8, 15, 17)
In the given diagrams, find the value of x in each case.
