Question

Please match the proof​

Answer 1

Δ ABC
`\sim` Δ DEF

Explanation:

Given:

`(AB)/(DE) = (AC)/(DF)= (BC)/(EF)`

W need to Prove Δ ABC
`\sim` Δ DEF

Solution:

Statement: Reason

`(AB)/(DE) = (AC)/(DF)= (BC)/(EF)` a) Given

"While Constructing both the triangle the lines were made parallel."

DE ║ AB c) Construction of Δ DEF on to Δ ABC

" When the Lines are parallel then their corresponding angles are equal in measure."

∠A ≅ ∠ EDF and ∠C ≅ ∠ EFD d) Corresponding Angles of parallel lines

Now By AA similarity theorem which states that;

"When 2 angles of one triangle are congruent to corresponding 2 angles of another triangle then 2 triangles are said to be similar."

Δ ABC
`\sim` Δ DEF b) By AA Similarity theorem.