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Q26.

Expert-verifiedFound in: Page 127

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: $\mathbf{\u25b3}\mathbf{ABF}$, $\mathbf{\u25b3}\mathbf{BCG}$**

**The diagram outlining the triangles listed is:**

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

The diagram outlining the triangles $\u25b3ABF$and$\u25b3BCG$is:

As, cube is having faces which congruent squares.

Therefore, $AB=BC=BF=CG$ and $\angle ABF=\angle BCG=90\xb0$

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

In the triangles $\u25b3ABF$ and $\u25b3BCG$, it can be seen that $AB=BC$, $\angle ABF=\angle BCG=90\xb0$ and $BF=CG$.

Therefore, the triangles $\u25b3ABF$ and $\u25b3BCG$ are the congruent triangles by using the SAS postulate.

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

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