CBSE Class 9 Mathematics Triangles Notes

IX

Mathematics

Chapter 7: Triangles

Chapter Notes

Top Definitions

1. Two figures are congruent, if they are of the same shape and of the same size.

2. Two figures are similar, if they are of the same shape but of different size.

3. SAS congruence rule: Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

4. ASA congruence rule: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle.

5. AAS congruence rule: Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal.

6. SSS congruent rule: If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

7. RHS congruence rule: 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.

8. A triangle in which two sides are equal is called an isosceles triangle.

Top Concepts

1. If two triangles ABC and PQR are congruent under the corresponding A ↔ P, B ↔Q and C ↔ R, then symbolically, it is expressed as Δ ABC @ Δ PQR.

2. Two circles of the same radii are congruent.

3. Two squares of the same sides are congruent.

4. Each angle of an equilateral triangle is of 60°.

5. In congruent triangles corresponding parts are equal and we write this as ‘CPCT’ for corresponding parts of congruent triangles.

6. SAS congruence rule holds but not ASS or SSA rule.

7. Angles opposite to equal sides of an isosceles triangle are equal.

8. The sides opposite to equal angles of a triangle are equal.

9. RHS stands for Right Angle – Hypotenuse – Side.

10. If two sides of a triangle are unequal, then the greater angle is opposite to the greater side.

11. If two angles of a triangle are unequal, the greater side is opposite to the greater angle.

12. The sum of any two sides of a triangle is greater than the third side.

13. The difference between any two sides of a triangle is less than the third side.

14. If the sum of two adjacent angles is 180°, then the non – common arms of the angles form a line.  

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