Question

Copy each three-dimensional figure and with coloured pencils outline the triangles listed. What postulate proves that these triangles are congruent?

Given: Cube whose faces are congruent squares.

Show: $\mathbf{△}\mathbf{ABF}$,$\mathbf{△}\mathbf{BCG}$

Short answer

The diagram outlining the triangles listed is:

The postulate that proves the given triangles are congruent is SAS postulate.

Step-by-step solution

- Draw the labelled diagram outlining the triangles △ABF and △BCG.

The diagram outlining the triangles $△ABF$and$△BCG$is:

- Description of step.

As, cube is having faces which congruent squares.

Therefore, $AB=BC=BF=CG$and $\angle ABF=\angle BCG=90°$

That implies, $AB\cong BC\cong BF\cong CG$and $\angle ABF\cong \angle BCG$.

- Description of step.

In the triangles$△ABF$ and $△BCG$, it can be seen that $AB=BC$, $\angle ABF=\angle BCG=90°$ and $BF=CG$.

Therefore, the triangles$△ABF$ and$△BCG$ are the congruent triangles by using the SAS postulate.

- Write the conclusion.

The postulate that proves the given triangles are congruent is SAS postulate.