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Chapter 4: Q26. (page 127)

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: 鈻�ABF,鈻�BCG

Short Answer

Expert verified

The diagram outlining the triangles listed is:

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

Step by step solution

01

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

The diagram outlining the triangles 鈻�ABFand鈻�BCGis:

02

- Description of step.

As, cube is having faces which congruent squares.

Therefore, AB=BC=BF=CGand 鈭�ABF=鈭�BCG=90掳

That implies, AB鈮�BC鈮�BF鈮�CGand 鈭�ABF鈮�鈭�BCG.

03

- Description of step.

In the triangles鈻�ABF and 鈻�BCG, it can be seen that AB=BC, 鈭�ABF=鈭�BCG=90掳 and BF=CG.

Therefore, the triangles鈻�ABF and鈻�BCG are the congruent triangles by using the SAS postulate.

04

- Write the conclusion.

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

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