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Expert-verified Found in: Page 127 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # 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: $\mathbf{△}\mathbf{ABF}$, $\mathbf{△}\mathbf{BCG}$

The diagram outlining the triangles listed is: The postulate that proves the given triangles are congruent is SAS postulate.

See the step by step solution

## Step 1 - Draw the labelled diagram outlining the triangles △ABF and △BCG.

The diagram outlining the triangles $△ABF$and$△BCG$is: ## Step 2 - 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 $\angle ABF\cong \angle BCG$.

## Step 3 - 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.

## Step 4 - Write the conclusion.

The postulate that proves the given triangles are congruent is SAS postulate. ### Want to see more solutions like these? 