Hg
Name: Class 9
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The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
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Triangles
Properties of Triangles:
• Isosceles Triangle - A triangle whose two sides are equal is called an isosceles triangle.
• Equilateral Triangle - A triangle whose all 3 sides are equal is called an equilateral triangle. Each angle
of an equilateral triangle is 60
o
.
• Interior angle property - Sum of all 3 interior angles of a triangle is 180
o
.
• Exterior angle property – An exterior angle of a triangle = sum of its interior opposite angles.
• Sum of the 3 exterior angles of a triangle is 360
o
.
• Angles opposite to equal sides of a triangle are equal and conversely,
sides opposite to equal angles of a triangle are equal.
i.e. If AB = AC => B = C and vice versa.
• Sides opposite to greater angle of a triangle is greater. i.e., if in above figure if B > C then AC > AB.
• The sum of any two sides of a triangle > 3
rd
side i.e., AB + BC > CA, BC + CA > AB & CA + AB > BC
• The difference any of two sides of a triangle < 3
rd
side. i.e., AB – BC < CA, BC – CA < AB & zCA – AB < BC
Congruency:
• Two figures are congruent if they are of same size and shape i.e., they are identical in all respects.
• If two triangles ABC and PQR are congruent under the correspondence A P, B Q and C R, then
symbolically, it is expressed as ∆ ABC ∆ PQR.
• Congruency Rules for triangles –
o SSS (Side Side Side) – If three sides of one triangle are equal to the three sides of another
triangle
o SAS (Side Angle Side) – If two sides and included angle of one triangle are equal to the 2 sides
and included angle of another triangle
o ASA (Angle Side Angle) – If two angles and included side of one triangle are equal to the 2
angles and included side of another triangle
o AAS (Angle Angle Side) – If two angles and one side of one triangle are equal to the 2 angles and
one side of another triangle
o RHS (Right angle Hypotenuse Side) – If in two right triangles, hypotenuse and one side of one
triangle are equal to hypotenuse and one side of another triangle
• If two triangles are congruent, then corresponding parts are equal. In other words, Corresponding
Parts of Congruent Triangles (CPCT) are equal.
