Triangles
Class 9 NCERT
Congruence
- equal in all respects - in both shape and size
- for triangles, equal in sides and angles
- one to one correspondence
- symbol
- CPCT - corresponding parts of congruent triangles
- all congruent figures are similar but not vice versa
Similarity
- number of sides equal
- all corresponding anges are equal
- all corresponding sides are in same ratio or proportion
Criteria
- SAS
- ASA
- AAS
- SSS
RD Sharma (new)
- BPT theorem or Thales theorem
- find the missing side
- find the ratio
- prove the theorem
- prove the similarity of the figures
- if AD is the bisector of angle A and meets the side BC at D, find the missing side - take the triangles are similar and apply the BPT theorem
- ratio of perimeter of similar triangles are equal with the ratio of corresponding sides
- a girl of height 90cm is walking away from the base of a lamp post at a speed of 1.2 m/sec. If the lamp os 3.6 m above ground, find the length of her shadow after 4 seconds
- distance covered in 4 seconds = 1.2 * 4 = 4.8 m
- the girl height and the lamp post are parallel
- therefore both the triangles are similar
- it is taken that the shadow is formed infront of the girl, that is away from the lamp post
- using similarity rule for sides, find the shadow length
