An important question from ML aggarwal of Similarities in which are to calculate the length of AC and EF, if AB,EF and CD are parallel lines and AB=15 cm,EG=5 cm,GC=10 cm and DC=18cm
ML Aggarwal Avichal publication class 10, Similarity question no 20a
Consider △EFG and △GCD
EF∥CD
⟹∠GCD=∠GEF (∵ alternative angles )
∠FGE=∠CGD (∵ vertically opposite angles )
as two angles are equal automatically third angle will be equal
So by AAA criteria , we get △EFG∼△CDG
⟹EF/EG=CG/CD
​⟹EF=5×18/10​=9 cm
AB∥EF
⟹∠BAC=∠FEC,∠ABC=∠EFC and ∠C remains the same
So by AAA criteria ,we get
△ABC∼△EFC
⟹AC/AB​=EC/EF
​⟹AC=15×15/9​=25 cm