# Selina Solutions Class 9 Mathematics Solutions for Exercise 9(B) in Chapter 9 - Chapter 9- Triangles [Congruency in Triangles]

Question 7 Exercise 9(B)

ABCD is a parallelogram. The sides AB and AD are produced to E and F

respectively, such that AB=BE and AD=DF.

Prove that: 𝚫BEC≅ 𝚫DCF

Solution

Video transcript
"hello students my name is rabbit singh and i welcome you all to leader learning homework one of india's best online classes now today in this video we have a question that is based on the topic of parallelogram the question says abcd is a parallelogram the sides a b and adr produced to e and f now let us label it as this is a b c and d now sides a b a b is produced to e and this is produced to a d is produced to f respectively such that a b this is equal to b e that means this so similarly it is showing that b is the midpoint of a e and a d is equal to df so d is a midpoint of af now we know angle bad is equal to angle cdf how angle ba d this angle is equal to angle c d f how corresponding angles for parallel lines if you check they are corresponding angles of parallel lines a b and c d this is a d this is a b and this is c d these are parallel lines and also this parallelogram so obviously uh opposite sides are parallel now again if you check angle bad angle b a d this angle is equal to angle c b e again this part same thing corresponding angles for a b and c d a b and c d now does angle c d f is equal to angle c b this is one now a d is equal to b c opposite sides of parallelogram are equal so a d will become equal to b c a d is equal to df that is already given df is equal to fc now based on that if you check ad is equal to 80 left hand side equal to bc will become equal to dm hence first part proof similarly we will prove b e is equal to c d b is equal to b e is equal to c d this side now in triangle cdf c d f this triangle and triangle cpe this triangle this we have already proved from one this part fd is equal to bc from two here third be is equal to cd from third so based on that triangles are congruent to each other how this is angle this is side and this is side so based on sas criterion they are congruent so triangle b e c is congruent to triangle dcf so what we have to prove so we have proved that science we will write here hence proved so i think i hope you have understood the concept very clearly but still if you have any doubt do comment in the comment box and please like and subscribe our channel for lido thank you"
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