- Books Name
- CBSE Class 7 Mathematics Book
- Param Publication
- CBSE Class 7
Angle Sum Property of a Triangle:
The sum of the measures of three angles of a triangle is 180°.
Proof of Angle Sum Property of a Triangle
Given : A triangle ABC.
To prove : ∠ A +∠B +∠C = 180°
Construction : Draw a line segment PQ through A and parallel to BC.
Proof: Mark the angles as indicated in the figure.
Hence, ∠ A +∠B +∠C = 180°
or sum of the angles of a triangle is 180°
ANGLE BISECTORS OF A TRIANGLE AND IN-CENTRE
Angle Bisectors :-
Angle bisector of a triangle is a line segment which bisect the angle and whose end points lies on the vertex and its opposite side.
• In the given figure, AD is the bisector of
So ∠BAD = ∠DAC
• In-centre is the meeting point of all three angle bisectors of a triangle.
• In the given figure, I is the Incentre of ∆
• In-centre always lies inside the triangle.
• The perpendicular distance from incentre to the side of triangle is always same.
⇒ IP = IQ = IR
• A circle can be drawn inside the triangle by assuming I as centre and IP as radius.
PERPENDICULAR BISECTOR AND CIRCUMCENTRE
It is a line segment which is perpendicular to the side of a triangle and passing through the mid point of the side.
In the given figure MN is the perpendicular bisector for ∆