Page 185 - Maths Skills - 7

The Triangle and Its Properties 183

MIND MAP

The Triangle and Its Properties

Properties Important Terms

1. ANGLE SUM PROPERTY A 1. MEDIAN OF A TRIANGLE
In a triangle, AD, BE, FC are medians of triangle ABC
∠A + ∠B + ∠C = 180° i.e. BD = DC
“Sum of all the interior FB = AF A Centroid
angles of a triangle is 180.” B C AE = EC F E
2. EXTERIOR ANGLE PROPERTY
“If a side of a triangle is produced then the B D C
exterior angle is equal to the sum of two
interior opposite angles.” 2. ALTITUDE OF A TRIANGLE
Here, AD, FC, BE are the perpendicular to the
A corresponding sides
1 i.e. AD ⊥ BC A
BE ⊥ AC E
2 3 4 FC ⊥ AB F Orthocentre
B C D P
i.e., ∠4 = ∠1 + ∠2
B D C
3. TRIANGLE INEQUALITY PROPERTY
“The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.” A
i.e., a + b > c
or a + c > b or b + c > a c b

4. PYTHAGORAS THEOREM B a C
AB + BC = AC 2 Rememberable Points
2
2
Sum of all the interior angles
A
in any polygon = (2n – 4) × 90°
Hypotenuse Where, n is the number of
Perpendicular
90° sides in that polygon.
B C
Base