Question

Please match the proof​

Answer 1

Answer:

Δ ABC $\sim$ Δ DEF

Step-by-step explanation:

Given:

$\frac{AB}{DE} = \frac{AC}{DF}= \frac{BC}{EF}$

W need to Prove Δ ABC $\sim$ Δ DEF

Solution:

Statement:                                                  Reason

$\frac{AB}{DE} = \frac{AC}{DF}= \frac{BC}{EF}$                    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.