Polygons

1003021307

Level: 
A
Choose the wrong claim:
The diagonals of a rhombus contain an acute angle.
In each parallelogram the opposite angles are congruent.
If one of the interior angles of a quadrilateral is greater than straight angle, the quadrilateral is not convex.
All interior angles in a square are right.

1003021308

Level: 
A
Choose the wrong claim:
The sum of the opposite angles in a rectangle is \( 360^{\circ} \).
The sum of the interior angles of a convex n-gon is \( (n-2)\cdot180^{\circ} \).
If there is just one pair of sides parallel in a quadrilateral and the other side is perpendicular to them, then the quadrilateral is a right-angled trapezium.
At least one of the interior angles in a trapezium is obtuse.

1103021303

Level: 
A
A rectangle with sides \( a \), \( b \) is given. The angle between diagonals \( \alpha = 60^{\circ} \). The longer side \( a = 6\,\mathrm{cm} \). Calculate the length of the shorter side \( b \).
\( \frac6{\sqrt3}\,\mathrm{cm} \)
\( \frac3{\sqrt3}\,\mathrm{cm} \)
\( \frac1{\sqrt3}\,\mathrm{cm} \)
\( 6\sqrt3\,\mathrm{cm} \)