all know, a triangle is a shape that consists of three sides and three angles.
Taking a look at the triangle’s angles often helps us find out what kind of
triangle we are dealing with.
are some facts to remember:
- The three angles
in a triangle always add up to 1800
- The three angles
of an equilateral triangle are all equal to 600
- Two angles of an
isosceles triangle are equal.
- One angle of a
right-angled triangle is 900
- All angles of an
acute-angled triangle are acute angles, thus smaller than 900
- One angle of an
obtuse-angled triangle is obtuse, thus larger than 900 and
smaller than 1800
triangles are congruent they have equal sides, equal areas.
corresponding sides and included
angle of the other triangle, then both triangles are congruent.
AB = DE, BC = EF and ∠B = ∠E,
then ΔABC≈ΔDEF2. ASA condition
If two angles and the included side of one triangle is equal to the
corresponding two angles and the
included side of the other triangle, then both triangles are congruent.
If ∠A = ∠D, ∠B
= ∠E and AB = DE, then ΔABC≈ΔDEF3. SSS condition
three sides of one triangle is equal to the corresponding three sides of other
triangle then both triangles are
two triangles are right-
angled triangle and hypotenuse and one side of one
triangle is equal to the
hypotenuse and corresponding side of other triangle, then both triangles are
=∠E = 90°, AC = DF and AB = DE or BC = EF, then ΔABC≈ΔDEF
All the congruent triangles are similar but all similar triangles are
The ratio of the areas of two similar triangles is equal to the ratio of
the squares of any two corresponding sides.
following four theorems are most important in solving questions on triangles.Pythagoras’ theorem: In a right angle triangle the square of the
hypotenuse is equal to the sum of the squares of other two sides.
Pythagorean triplet: There are certain triplets which satisfy the pythagoras’
theorem and are commonly, called pythagorean triplet.
For example: 3, 4, 5;
5, 12, 13; 24, 10, 26; 24, 7, 25;
15, 8, 17Appolonious theorem:
proportionality and Mid Point theorem:
first triangle, DE // BC so AD/DB=AE/EC
second triangle, D and E are mid points of AB and AC respectively. Which