IX Triangle cbse congruence of triangle and criteria application
- 4. 6 cm 9 cm 9.5 cm 9.5 cm X Non- identical Identical
- 5. Congruent figures Equal in all respects or figures whose shapes and sizes are both the same Congruent Congruent
- 6. Congruence in real life
- 8. 5 cm 5 cm 7 cm Congruent line segments
- 9. 4 cm 4 cm 6 cm 8 cm Congruent circles
- 10. Congruent squares Congruent triangles 5 cm 5 cm 7 cm 7 cm
- 13. A B C Vertices Sides Angles AB ,BC, CA A,B,C ∠A, B, ∠ C ∠
- 14. A B C P Q R 16 cm 16 cm
- 15. A B C P Q R
- 17. A B C P Q R 4 c m 5 cm 4 c m 4.5 cm 5 cm 4.5 cm
- 19. Check whether the following triangles are congruent P Q R P Q R P Q R 23 cm 23 cm 23 cm 23 cm 23 cm 2 3 c m 600 60 0 600 600 6 0 0 60 0 800 700 300 750 600 500 700 400 600 500 24 cm 1 6 c m 21 cm 1 4 c m 21 cm 18 cm 750 650 400 400 650 14 cm 14 cm 14 cm 25 cm 18 cm 8 cm 300 700 800 7 cm 7 cm 5 cm 5 cm 3 cm 3 c m
- 20. Criteria for congruence of Triangles
- 21. Criteria for congruence of Triangles SAS Congruence rule A B C P Q R 7 cm 7 cm 9 cm 9 cm 500 500
- 22. 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.
- 23. ASA Congruence rule 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.
- 24. AAS Congruence rule Two triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal.
- 25. 5 m 5 m 7 m 7 m 25 cm Check whether the following triangles are congruent 25 cm 21 cm 21 cm 3 1 c m 31 cm 500 500 600 500 4 00 700 4 00 700 450 450 500 600 500 500
- 26. A B C D A B C D
- 27. SAS Congruence rule ASA Congruence rule AAS Congruence rule
- 28. 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?
- 29. 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 ∠ ∠
- 30. 3. AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.
- 31. 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. ≅
- 32. 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. ∠
- 33. 6. In Fig. 7.21, AC = AE, AB = AD and BAD = EAC. Show ∠ ∠ that BC = DE
- 34. 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
- 35. 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 2 AB