Question

Fill in the blanks in the following proof.

Answer 1

Table :

Statements Reasons

1)ΔEGC≅ΔEGB Given

2)EB = EC Corresponding Parts of Congruent

Triangles are Congruent

3) BC = BE Given

4) By 2 and 3 EB≅EC≅BC

5)∠BEC = 60° ΔBEC is an equilateral triangle

Explanation:

We are given that BE = BC ---1

We are also given that ΔEGC≅ΔEGB

So, BE = CE(Corresponding Parts of Congruent Triangles are Congruent) ---2

Now By 1 and 2

BE=BC=CE

In ΔBEC

BE=BC=CE

Since all sides are equal . So, it is an equilateral triangle

All angles of equilateral triangle are also equal i.e. 60°

So, ∠BEC = 60°

Hence proved

Table :

Statements Reasons

1)ΔEGC≅ΔEGB Given

2)EB = EC Corresponding Parts of Congruent

Triangles are Congruent

3) BC = BE Given

4) By 2 and 3 EB≅EC≅BC

5)∠BEC = 60° ΔBEC is an equilateral triangle