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

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

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

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-: Select Topics :-

Exercise-8(a)

Exercise-8(b)

Exercise-8(c)

Chapter Test

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Exercise-8

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

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.

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.

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Exercise-8.(a)

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

Question 1:

In the figure, AB and CD bisect each other at K. Prove that AC= BD.

…………………..

 

Question 2:

In the figure, the sides BA and CA have been produced such that BA = AD and CA = AE prove that DE || BC.

Question 3:

……………………

……………………

…………………..

………………….

Question 19:

Find the value of x and y in the figure given below using congruency of triangles.

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Exercise-8.(b)

Triangles Class-9 S.Chand ICSE Maths Ch-8

Question 1:

The vertical angle of an isosceles triangle is 90 degree. Find of its base angle.

Question 2:

Prove that each angle of an ……………….. triangle ?

Question 3:

Prove that if the  base of an ……….. equal to each other ?

Question 4:

……………………

……………………..

…………………….

Question 20:

If the bisector of the vertical angle of a triangle bisects the base also, the triangle is isosceles.

…………………..

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Exercise-8.(c)

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

Question 1:

In a triangle PQR, side PQ is …………………… prove that

(i) PS > RS

(ii) PS > PR

Question 2:

In a Triangle PQR , ………….. order PX, QX, RX.

Question 3:

…………………….

…………………….

…………………..

Question 19:

Prove that in a triangle, the difference of any two side in less than the third side.

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Chapter Test

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

Question 1:

(i) Which of the following is not a criterion for congruency of triangles ?

………………….

(ii) Which congruence statement correctly indicates that the two given triangles are congruent ?

………………….

Question 2:

…………………….

………………………

…………………….

Question 6:

Two side of a triangle are of lengths 4 cm, and 10 cm, If the lengths of the third side is q cm then

,…………………..

— : 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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