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Congruency, SMB-013

Which two of the triangles below are congruent?   (2 marks)

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\(\text{Triangle B and Triangle C}\)

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\(\text{Unknown side}\ (x)\ \text{in Triangle B (Pythagoras):}\)

\(x=\sqrt{11^2-(\sqrt{96})^2} = \sqrt{25} = 5\)

\(\Rightarrow\ \text{Triangle B and Triangle C are congruent (SSS)} \)

\(\text{Triangle A can be shown to have different dimensions but this is not necessary.}\)

Congruency, SMB-012

Which two of the triangles below are congruent?   (2 marks)

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\(\text{Triangle A and Triangle C}\)

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\(\text{Unknown side}\ (x)\ \text{in Triangle A (Pythagoras):}\)

\(x=\sqrt{8^2-(\sqrt{48})^2} = \sqrt{16} = 4\)

\(\Rightarrow\ \text{Triangle A and Triangle C are congruent (SSS)} \)

\(\text{Triangle B can be shown to have different dimensions but this is not necessary.}\)

Congruency, SMB-008

In the figure below, \(ABCD\) is a parallelogram where opposite sides of the quadrilateral are equal.
 

Prove that a diagonal of the parallelogram produces two triangles that are congruent.  (2 marks)

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\(\text{Proof (See Worked Solutions)}\)

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\(\text{One of multiple solutions:}\)

\( AB=CD\ \ \text{and}\ \ AC=BD\ \ \text{(given)} \)

\(BC\ \text{is common} \) 

\(\therefore\ \Delta ABC \equiv \Delta DCB\ \ \text{(SSS)}\)

Congruency, SMB-002

The diagram shows two triangles that touch at the middle of a circle.

Prove that this pair of triangles are congruent.  (2 marks)

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\(\text{Proof (See Worked Solutions)}\)

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\(\text{Base of each triangle (chords) are equal} \)

\(\text{All other sides are equal radii of the circle} \)

\(\therefore\ \text{Two given triangles are congruent}\ \ \text{(SSS)}\)