If two triangles are congruent
they have equal sides, equal areas.
Condition for Congruence
SAS Theorem:
If two sides and the angle between these two sides (included angle) of one triangle are congruent to the corresponding two sides and the included angle of a saecond triangle, then the two triangles are congruent
Example:
If two sides and the angle between these two sides (included angle) of one triangle are congruent to the corresponding two sides and the included angle of a saecond triangle, then the two triangles are congruent
Example:
AAS Theorem:
If two angles and a side not between these two angles of one triangle are congruent to two angles and the corresponding side not between these two angles of a second triangle, then the two triangles are congruent
Example:
Hypotenuse-Leg Theorem:
If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and corresponding leg of a second right triangle, then the two triangles are congruent
Example:
Pythagoras’ Theorem: In
a right angle triangle the square of the hypotenuse is equal to the sum of the
squares of other two sides.
b2=a2+c2
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, 17
Appolonious Theorem:
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, 17
Appolonious Theorem:
In triangle ABC, AD is median,
which divides BC into two equal parts. Then,
AB2+AC2=2(AD2+BD2)=2(AD2+DC2)
Stewart theorem:
In Triangle ABC, AD divides side
BC in the ratio m and n. (Here AD need not be median) then,
m.b2+n.c2=a(d2+mn)
Mean proportionality and Mid
Point theorem:
In the first triangle, DE // BC
so AD / DB = AE / EC
In the second triangle, D and E
are mid points of AB and AC respectively. Which implies,
AD / DB = AE / EC = 1
AD / DB = AE / EC = 1
Also, DE = 1 / 2 BC