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Prove similarity theorem

CLASS 10

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Answered by pkparmeetkaur
3
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Given : Two triangles ABC and DEF such thatAB BC CA 
---- = ------ = ------
DE EF FD

Prove that : ΔABC ~ ΔDEF 

Construction : Let P and Q be two points on DE and DF respectively such that DP = AB and DQ = = AC. Join PQ.

Statements Reasons

1)  AB        AC  1) Given
    ---- = ------ 
      DE      DF

2)   DP       DQ   2) As AB = DP and AC =DQ.
   ---- = ------  By substitution
      DE       DF

3) PQ || EF 3) By converse of basic
proportionality theorem

4) ∠DPQ = ∠E and ∠DQP = ∠F

4) Corresponding angles

5) ΔDPQ ~ ΔDEF 5) By AA similarity

6) DP PQ  6) By definition of similar triangles
---- = ------ 
DE EF

7) AB PQ 
---- = ------  7) As DP = AB , by substitution
DE EF

8)  PQ      BC  8) From (1) (6) and (7)
   ---- = ------ 
    EF     EF

9) PQ = BC 9) From (8)

10) ΔABC ≅ ΔDPQ 10) By S-S-S postulate

11) ΔABC ~ ΔDEF 11) From (5) and (10)
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Answered by BrainlyHeart751
3

Answer:

Step-by-step explanation:

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