Q8) EX 7.1 Class 9 Maths Chapter 7 Triangles | Maths Class 9 NCERT CBSE Solutions By Apni ClassRoom

Q8) EX 7.1 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 #mathsclass9th #TrianglesMathsClass9th #mathsclass9thChapeter7th #TrianglesInMathsClass9th class 9th exercise 7.1 question number 8, class 9 maths chapter 7 triangles exercise 7.1 question 8, class 9th ncert maths chapter 7 triangles exercise 7.1 question 8, triangles exercise 7.1, triangles class 9 ncert, triangles class 9 maths, 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. 15. Sum of any two sides of a triangle is greater than the third side. EXERCISE 7.1 1. In quadrilateral ACBD,AC = AD and AB bisects ? A (see Fig. 7.16). Show that ? ABC ? ? ABD. What can you say about BC and BD? 2. ABCD is a quadrilateral in which AD = BC and ? DAB = ? CBA (see Fig. 7.17). Prove that (i) ? ABD ? ? BAC (ii) BD = AC (iii) ? ABD = ? BAC. 3. AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB. 4. l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that ? ABC ? ? CDA. 5. Line l is the bisector of an angle ? A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ? A (see Fig. 7.20). Show that: (i) ? APB ? ? AQB (ii) BP = BQ or B is equidistant from the arms of ? A. 6. In Fig. 7.21, AC = AE, AB = AD and ? BAD = ? EAC. Show that BC = DE. 7. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ? BAD = ? ABE and ? EPA = ? DPB (see Fig. 7.22). Show that (i) ? DAP ? ? EBP (ii) AD = BE 8. In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see Fig. 7.23). Show that: (i) ? AMC ? ? BMD (ii) ? DBC is a right angle. (iii) ? DBC ? ? ACB (iv) CM = 1/2AB