IX Triangle cbse congruence of triangle and criteria application

Know about triangle

1. TRIAGNLES CHAPTER 7

2. Identical Identical

3. 6 cm 9 cm 9.5 cm 9.5 cm X Non- identical Identical

4. Congruent figures Equal in all respects or figures whose shapes and sizes are both the same Congruent Congruent

5. Congruence in real life

6. Are they congruent?

7. 5 cm 5 cm 7 cm Congruent line segments

8. 4 cm 4 cm 6 cm 8 cm Congruent circles

9. Congruent squares Congruent triangles 5 cm 5 cm 7 cm 7 cm

10. Congruence of triangles

11. A B C Vertices Sides Angles AB ,BC, CA A,B,C ∠A, ∠B, ∠C

12. A B C P Q R 16 cm 16 cm

13. A B C P Q R

14. A B C P Q R 4 cm 5 cm 4 cm 4.5 cm 5 cm 4.5 cm

15. Are they congruent?

16. 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 23 cm                                 24 cm 16 cm 21 cm 14 cm 21 cm 18 cm           14 cm 14 cm 14 cm 25 cm 18 cm 8 cm       7 cm 7 cm 5 cm 5 cm 3 cm 3 cm

17. Criteria for congruence of Triangles

18. Criteria for congruence of Triangles SAS Congruence rule A B C P Q R 7 cm 7 cm 9 cm 9 cm    

19. 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.

20. 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 .

21. AAS Congruence rule T wo triangles are congruent if any two pairs of angles and one pair of corresponding sides are equal .

22. 5 m 5 m 7 m 7 m 25 cm Check whether the following triangles are congruent 25 cm 21 cm 21 cm 31 cm 31 cm                            

23. A B C D A B C D

24. SAS Congruence rule ASA Congruence rule AAS Congruence rule

25. 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?

26. 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

27. 3. AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

28. 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.

29. 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.

30. 6. In Fig. 7.21, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Show that BC = DE

31. 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 ∆ DAP ≅ ∆ EBP ( ii) AD = BE

32. 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: ∆ AMC ≅ ∆ BMD ( ii) ∠ DBC is a right angle ( iii) ∆ DBC ≅ ∆ ACB ( iv) CM = 1 2 AB