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Properties of Geometric Figures, SM-Bank 031 MC

The diagram of a quadrilateral is shown below. 
 

Which name below does not refer to the quadrilateral in the diagram?

  1. quadrilateral \(CDAB\)
  2. quadrilateral \(BCDA\)
  3. quadrilateral \(CBAD\)
  4. quadrilateral \(CBDA\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Vertices need to be named in order (either clockwise or counter clockwise)}\)

\(CBDA\ \text{is not correct as vertex}\ B\ \text{and}\ D\ \text{are not adjacent.}\)

\(\Rightarrow D\)

Properties of Geometric Figures, SM-Bank 044

Complete the table below by placing a tick or a cross in the appropriate box to indicate which properties belong to different quadrilaterals.   (3 marks)

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Rhombus} & \textbf{Trapezium} & \textbf{Rectangle}  \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} &  &  &  \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are equal} \rule[-1ex]{0pt}{0pt} &  &  &  \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} &  &  &  \\
\hline
\end{array}

Show Answers Only

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Rhombus} & \textbf{Trapezium} & \textbf{Rectangle}  \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \cross \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are equal} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\end{array}

Show Worked Solution

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Rhombus} & \textbf{Trapezium} & \textbf{Rectangle}  \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \cross \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are equal} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\end{array}

Properties of Geometric Figures, SM-Bank 043

Complete the table below by placing a tick or a cross in the appropriate box to indicate which properties belong to different quadrilaterals.   (3 marks)

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Square} & \textbf{Kite} & \textbf{Parallelogram}  \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} &  &  &  \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals bisect each other} \rule[-1ex]{0pt}{0pt} &  &  &  \\
\hline
\rule{0pt}{2.5ex} \text{Two pairs of equal adjacent sides} \rule[-1ex]{0pt}{0pt} &  &  &  \\
\hline
\end{array}

Show Answers Only

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Square} & \textbf{Kite} & \textbf{Parallelogram}  \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals bisect each other} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Two pairs of equal adjacent sides} \rule[-1ex]{0pt}{0pt} & \checkmark & \checkmark & \cross \\
\hline
\end{array}

Show Worked Solution

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Square} & \textbf{Kite} & \textbf{Parallelogram}  \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals bisect each other} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Two pairs of equal adjacent sides} \rule[-1ex]{0pt}{0pt} & \checkmark & \checkmark & \cross \\
\hline
\end{array}

Properties of Geometrical Figures, SM-Bank 042

Complete the table below by placing a tick or a cross in the appropriate box to indicate which properties belong to different quadrilaterals.   (3 marks)

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Trapezium} & \textbf{Rectangle} & \textbf{Rhombus}  \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\end{array}

Show Answers Only

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Trapezium} & \textbf{Rectangle} & \textbf{Rhombus}  \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \cross \\
\hline
\end{array}

Show Worked Solution

\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Trapezium} & \textbf{Rectangle} & \textbf{Rhombus}  \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \cross \\
\hline
\end{array}

Special Properties, SMB-013 MC

Which statement is always true?

  1. Scalene triangles have two angles that are equal.
  2. All angles in a parallelogram are equal.
  3. The opposite sides of a trapezium are equal in length.
  4. The diagonals of a rhombus are perpendicular to each other.
Show Answers Only

`D`

Show Worked Solution

`text{Consider each option:}`

`A:\ \text{Isosceles (not scalene) have two equal angles.}`

`B:\ \text{Only opposite angles in a parallelogram are equal.}`

`C:\ \text{At least one pair of opposite sides of a trapezium are not equal.}`

`D:\ \text{Rhombuses have perpendicular diagonals.}`

`=>D`

Special Properties, SMB-010 MC

Which of these are always equal in length?

  1. the diagonals of a rhombus
  2. the diagonals of a parallelogram
  3. the opposite sides of a parallelogram
  4. the opposite sides of a trapezium
Show Answers Only

`C`

Show Worked Solution

`text{Consider each option:}`

`A:\ \text{rhombus diagonals are perpendicular but not always equal}`

`B:\ \text{parallelogram diagonals not always equal (see below)}`

`C:\ \text{always true (see above)}`

`D:\ \text{at least 1 pair of opposite sides of a trapezium are not equal}`
\(\Rightarrow C\)

Special Properties, SMB-009 MC

`PQRS` is a parallelogram.

Which of these must be a property of `PQRS`?

  1. Line `PS` is perpendicular to line `PQ`.
  2. Line `PQ` is parallel to line `PS`.
  3. Diagonals `PR` and `SQ` are perpendicular.
  4. Line `PS` is parallel to line `QR`.
Show Answers Only

`D`

Show Worked Solution

`text{By elimination:}`

`A\ \text{and}\ B\ \text{clearly incorrect.}`

`C\ \text{true if all sides are equal (rhombus) but not true for all parallelograms.}`

`text(Line)\ PS\ text(must be parallel to line)\ QR.`

`=>D`