OP Malhotra Notes on Triangles Class-9 S.Chand ICSE Maths Ch-8. We Provide notes on it and Step by Step Answer of Exe-8(a), Exe-8(b), Exe-8(c), with Chapter Test of S Chand OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-9.

OP Malhotra Triangles Class-9 S.Chand ICSE Maths Ch-8 Notes

Criteria for Congruency :

The following are the criteria for the congruency of the triangles.

SSS Criteria for Congruency :

• If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
• If all sides are exactly the same, then their corresponding angles must also be exactly the same.

SAS Criteria for Congruency :

– Axiom: Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

ASA Criteria for Congruency :

– Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle

AAS Criteria for Congruency :

– Two triangles are said to be congruent to each other if two angles and one side of one triangle are equal to two angles and one side of the other triangle.

RHS Criteria for Congruency :

• If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.
• RHS stands for Right angle – Hypotenuse – Side.

Practice Questions on Criteria for Congruency :- Exercise-8(a)

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Properties of Isosceles triangle

– If 2 sides of the triangle are equal, the angles opposite those sides are also equal and vice versa.

NOTE :-

• Scalene Triangle – A triangle, no two of whose sides are equal, is called scalene triangle.
• Equilateral Triangle – A triangle whose all sides are equal, is calle an equilateral triangle.
• Right angled triangle – A triangle with one right angle is called a right angled triangle.
• The sum of all the angles of a triangle is 180^o.
• If a side of a triangle is produced, the exterior angle so formed is equal to the sum of two interior opposite angles.
• Angle opposite to equal sides of a triangle are equal.
• Sides opposite to equal angles of a triangle are equal.
• Each angle of an equilateral triangle is .
• If the altitude from one vertex of a triangle bisects the base, then the triangle is isosceles triangle.

Practice Questions on Properties of Isosceles Triangle :- Exercise-8(b)

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Proof and Finding Angles

Angle Sum Property : The sum of all interior angles in any triangle is exactly 180°.
Exterior Angle Theorem : The measure of an exterior angle of a triangle is equal to the sum of its two interior opposite angles.
Isosceles Triangle Property : Angles opposite to equal sides are equal. For instance, if side AB=AC, then ∠B = ∠C.
Equilateral Triangle Property : Every angle in an equilateral triangle is 60°.
Right-Angled Triangle : One angle is always 90°. If it is also isosceles, the other two angles are 45° each.

Practice Questions on Proof and Finding Angles :- Exercise-8(c)

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In this chapter, we study all the topics on Triangles and do some practice questions also. Here we solve extra practice questions on this chapter for better understanding.

Here is the link for extra practice questions on Triangles :- Chapter Test

— : End of Triangles  OP Malhotra S Chand Solutions :–

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Return to :–   OP Malhotra S Chand Solutions for ICSE Class-9 Maths

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