Question

Fill in the blanks in the following proof.

Answer 1

Answer:

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

Step-by-step 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