Question

In the figure, LABC=75° and LEDC=75°
state which two triangles are similar and by which test? also write the similarity of these two triangles by a proper one to one correspondence.

Answer 1

$\bold\pink{\fbox{\sf{Answer}}}$

Δ ABC  ≅  Δ EDC

AC/EC  = BC/DC= AB/ED  

$\bold\red{\fbox{\sf{ Solution}}}$

in Δ ABC

∠ABC = 75 °

∠BCA = x °

∠BAC = 180° - 75° - x° = 105 - x°

in Δ EDC

∠EDC = 75 °

∠ECD = x °

∠CED = 180° - 75° - x° = 105 - x°

∠ABC = ∠EDC

∠BCA = ∠ECD

∠BAC = ∠CED

All the angles are same so

Δ ABC  ≅  Δ EDC

AC/EC  = BC/DC= AB/ED

Answer 2

in Δ ABC

∠ABC = 75 °

∠BCA = x °

∠BAC = 180° - 75° - x° = 105 - x°

in Δ EDC

∠EDC = 75 °

∠ECD = x °

∠CED = 180° - 75° - x° = 105 - x°

∠ABC = ∠EDC

∠BCA = ∠ECD

∠BAC = ∠CED

All the angles are same so

Δ ABC ≅ Δ EDC

AC/EC = BC/DC= AB/ED