These comprehensive RBSE Class 9 Maths Notes Chapter 7 Triangles will give a brief overview of all the concepts.
RBSE Class 9 Maths Chapter 7 Notes Triangles
1. Congruency of Figures : If two geometrial figures are such that, when one of the figures is placed over the other, they cover each other completely, then the two figures are said to be congruent. Congruent means identically equal, i.e., figures with same shape and same size. This property of congruent figures is known as congruency.
2. Congruency of Triangles : Two triangles are congruent if and only if one of them can be made to superpose on the other, so as to cover it exactly. The symbol to show congruency is ≅. For example ΔABC ≅ ΔPQR is read as, “ΔABC is congruent to ΔPQR”.
3. Angle-Side-Angle Rule (ASA Rule) : Two triangles are congruent if two angles and the included side of one triangle is equal to two angles and the included side of other triangle. This result is the Angle-Side-Angle criterion for congruence and is written as ASA criterion.
4. Side-Angle-Side Rule (SAS Rule) : Two triangles are congruent if two sides and the included angle of one are equal to the corresponding sides and the included angle of the other triangle. This result is the Side-Angle-Side criterion for congruence and is written as SAS Rule.
5. Side-Side-Side Rule (SSSRule): If three sides of a triangle are equal to corresponding three sides of other triangle, then two triangles are congruent. (SSS Rule of congruency)
6. If two sides of a triangle are equal, then angles opposite to these sides are also equal.
Angles opposite to equal sides of an isosceles triangle are equal.
7. If two angles of a triangle are equal, then sides opposite to these angles are also equal.
8. Right angle-Hypotenuse-Side Rule (RHS 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. This congruency is known as “Right angle-Hypotenuse-Side” Rule. It is denoted as RHS Rule of congruency.
9. Inequality : When we compare two unequal things, then the relationship between them is known as an inequality relationship. An inequality says that two values are not equal.
10. Inequalities in a Triangle :
(i) If two sides of a triangle are unequal, the longer side has greater angle opposite it.
(ii) In a triangle the greater angle has the longer side opposite to it.
(iii) The sum of any two sides of a triangle is greater than the third side.
11. Two circles of same radius are congruent.
12. Two square of same sides are congruent.
13. If triangle ABC and PQR are congruent under the correspondence A ↔ P. B ↔ Q. C ↔ R, then in notation form they are written as ΔABC ≅ ΔPQR.
Note : It will be correct to write AABC ≅ AQRP or any such order.
14. Angles opposite to equal sides of a triangle are equal.
15. Sides opposite to equal angles of a triangle are equal.
16. Each angle of an equilateral triangle is 60°.
17. In a triangle, angle opposite to longer side is greater.
18. In a triangle, side opposite to greater angle is longer.