Скачать или смотреть Q6) EX 7.4 Class 9 Maths Chapter 7 Triangles | Maths Class 9 NCERT CBSE Solutions By Apni ClassRoom

Q6) EX 7.4 Class 9 Maths Chapter 7 Triangles | Maths Class 9 NCERT CBSE Solutions By Apni ClassRoom

Hello students, in this chapter you are going to learn triangles.

We will go topic wise

7. TRIANGLES
7.1 Introduction
7.2 Congruence of Triangles
7.3 Criteria for Congruence of Triangles
7.4 Some Properties of a Triangle
7.5 Some More Criteria for Congruence of Triangles
7.6 Inequalities in a Triangle

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Congruence of Triangles:
congruent’ means equal in all respects or figures whose shapes and sizes
are both the same).

Axiom 7.1 (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.

Theorem 7.1 (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.

Theorem 7.2 : Angles opposite to equal sides of an isosceles triangle are equal.
Theorem 7.3 : The sides opposite to equal angles of a triangle are equal.
Theorem 7.4 (SSS congruence rule) : If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
Theorem 7.5 (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.
Theorem 7.6 : If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).
Theorem 7.7 : In any triangle, the side opposite to the larger (greater) angle is longer.
Theorem 7.8 : The sum of any two sides of a triangle is greater than the third side.

In this chapter, you have studied the following points :
1. Two figures are congruent, if they are of the same shape and of the same size.
2. Two circles of the same radii are congruent.
3. Two squares of the same sides are congruent.
4. 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.
5. If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent (SAS Congruence Rule).
6. If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent (ASA Congruence Rule).
7. If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent (AAS Congruence Rule).
8. Angles opposite to equal sides of a triangle are equal.
9. Sides opposite to equal angles of a triangle are equal.
10. Each angle of an equilateral triangle is of 60°.
11. If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence Rule).
12. If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent (RHS Congruence Rule).
13. In a triangle, angle opposite to the longer side is larger (greater).
14. In a triangle, side opposite to the larger (greater) angle is longer.
EXERCISE 7.4
1. Show that in a right angled triangle, the hypotenuse is the longest side.
2. In Fig. 7.48, sides AB and AC of ? ABC are extended to points P and Q respectively. Also, ? PBC ? QCB. Show that AC AB.
3. In Fig. 7.49, ? B ? A and ? C ? D. Show that AD BC.
4. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD
(see Fig. 7.50). Show that ? A ? C and ? B ? D.
5. In Fig 7.51, PR PQ and PS bisects ? QPR. Prove that ? PSR ? PSQ.
6. Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.