KnowledgeBoat Logo
|

Mathematics

If Δ ABC ∼ Δ DEF, then

  1. ABEF=ACDF\dfrac{\text{AB}}{\text{EF}} = \dfrac{\text{AC}}{\text{DF}}

  2. ABDE=BCDF\dfrac{\text{AB}}{\text{DE}} = \dfrac{\text{BC}}{\text{DF}}

  3. ACDF=ABDE\dfrac{\text{AC}}{\text{DF}} = \dfrac{\text{AB}}{\text{DE}}

  4. BCEF=ACDE\dfrac{\text{BC}}{\text{EF}} = \dfrac{\text{AC}}{\text{DE}}

Similarity

6 Likes

Answer

ACDF=ABDE\dfrac{\text{AC}}{\text{DF}} = \dfrac{\text{AB}}{\text{DE}}

Reason

In Δ ABC ∼ Δ DEF, we can conclude :

AB corresponds to DE, BC corresponds to EF and AC corresponds to DF.

We know that,

Corresponding sides of similar triangles are equal.

∴ABDE=BCEF=ACDF⇒ABDE=ACDF.\therefore \dfrac{\text{AB}}{\text{DE}} = \dfrac{\text{BC}}{\text{EF}} = \dfrac{\text{AC}}{\text{DF}} \\[1em] \Rightarrow \dfrac{AB}{DE} = \dfrac{AC}{DF}.

Hence, option 3 is the correct option.

Answered By

3 Likes

Related Questions