Question

prove that if in two Triangles corresponding angles are equal then their corresponding sides are in the same ratio and hence the two Triangles are similar​

Answer 1

Step-by-step explanation:

Data: In a triangle ABC and DEF

angle A = angle D

angle B = angle E

angle C = angle F

To prove: AB/DE=AC/DF=BC/EF

Construction:Mark 'P'on DE and 'Q'on DE,join PQ

Proof: In a triangle ABC and triangle DPQ

angle A=angle D ( Data )

side AB=DP ( Construction )

side AC=DQ ( Construction )

triangle ABC is similar to triangle DPQ( SAS)

side BC=PQ ( CPCT ) equation 1

angle B = angle P ( CPCT )

angle B = angle E ( DATA )

therefore: PQ is parallel to EF ( axion1 )

DP/DE = DQ/DF = PQ/EF ( corollary of thales theorem )

therefore:AB/DE = AC/DF=BC/EF ( from equation 1 and construction )

HENCE PROVED

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