AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties

Students can go through AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties to understand and remember the concepts easily.

AP State Board Syllabus 7th Class Maths Notes Chapter 5 Triangle and Its Properties

→ Triangles can be classified according to properties of their sides and angles. Based on sides, triangles are of three types.

→ Equilateral triangle: A triangle in which all the three sides are equal is called an equilateral triangle. In △ABC
AB = BC = CA, also ∠A = ∠B = ∠C In an equilateral triangle each angle is equal to 60°.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 1

AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties

→ Isosceles triangle: A triangle in which two sides are equal is called an isosceles triangle.
In △PQR
PQ = PR also ∠Q = ∠R
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 1
The non-equal side in an isosceles triangle may be taken as base of the triangle.

→ Scalene triangle: A triangle in which no two sides are equal is called a scalene triangle.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 3
In △BAT
BA ≠ AT ≠ BT also ∠B ≠ ∠A ≠ ∠T.

→ Based on angles, triangles can be classified into three types.

→ Acute angled triangle: A triangle in which all the three angles are acute is called an acute-angled triangle.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 4
In △TAP,
∠T, ∠A, ∠P are acute angles.

→ Obtuse angled triangle: A triangle in which one angle is obtuse is called an obtuse angled triangle.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 5
In △FAN,
∠A is obtuse angle.
A triangle cannot have more than one obtuse angle,

→ Right angled triangle: A triangle in which one angle is a right angle is called a right angled triangle.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 6
In △COT
ZO is right angle (i.e) 90°.
A triangle cannot have more than one right angle,

AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties

→ Right angled isosceles triangle: A triangle in which one angle is right angle and two sides are equal is called a right angled isosceles triangle.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 7
In △POT,
PO = OT and ∠O = 90° also
∠P = ∠T = 45°

→ Family of triangles – Flow chart
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 8

→ Relation between sides of a triangle
In any triangle the sum of the lengths of any two sides is greater than the length of the third side.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 9
In △TIN,
TI + IN > TN; TN + NI > TI; TI + TN > IN
Also the difference between lengths of any two sides of the triangle is less than the length of the third side.
In △TIN, TI > TN – NI; IN > TI – TN; TN > IN – TI

AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties

→ Altitutes of a triangle
The length of a line segment drawn from a vertex to its opposite side and is perpendicular to it is called an altitude or height of the triangle. An altitude can be drawn from each vertex.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 10
Altitude of a triangle may be in its interior or exterior.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 11

→ Medians of a triangle
A line segment joining a vertex and the mid-point of its opposite side is called a median.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 12
A triangle has three medians.
The medians of a triangle are concurrent.
The point of concurrence of medians of a triangle is called the centroid of the triangle.
In △ABC, D, E and F are mid-points of the sides AB, BC and AC.
AE, CD and BF are mid-points.
G is the centroid.

AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties

→ Angle – sum property of a triangle: The sum of interior angles of a triangle is equal to 180° or two right angles.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 13
In △BET,
∠B + ∠E + ∠T = 180°

→ Exterior angle of a triangle

→ When one side of a triangle is produced, the angle thus formed is called an exterior angle.
AP Board 7th Class Maths Notes Chapter 5 Triangle and Its Properties 14
In △COL; the side OL is produced to D.
∠CLD is an exterior angle.
The exterior angle of a triangle is equal to the sum of the interior opposite angles.
∠COL + ∠OCL = ∠CLD