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.

1103021301

Level:
A
The sides of a rectangle are in the ratio $1:2$. Give the degree measure of the acute angle between the diagonals of the rectangle. Round the result to two decimal places.
$53.13^{\circ}$
$26.57^{\circ}$
$60^{\circ}$
$53^{\circ}$

1103021302

Level:
A
The aspect ratio of the sides of the $ABCD$ rectangle is $\sqrt3 : 1$. Express the degree measure of the obtuse angle contained by the diagonals of the rectangle.
$120^{\circ}$
$30^{\circ}$
$60^{\circ}$
$150^{\circ}$

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 $b$.
$\frac6{\sqrt3}\,\mathrm{cm}$
$\frac3{\sqrt3}\,\mathrm{cm}$
$\frac1{\sqrt3}\,\mathrm{cm}$
$6\sqrt3\,\mathrm{cm}$

1103021304

Level:
A
The side lengths of the rectangle $ABCD$ are in the ratio $5:12$. Give the degree measure of the angle $CAB$. Round the result to two decimal places.
$22.62^{\circ}$
$67.38^{\circ}$
$24.62^{\circ}$
$65.38^{\circ}$

1103021305

Level:
A
$ABCD$ is a square. Express the degree measure of the angle $EGD$ if the measure of the angle $CFG$ is $50^{\circ}$.
$5^{\circ}$
$10^{\circ}$
$15^{\circ}$
$20^{\circ}$

1103021306

Level:
A
In the square $ABCD$, $|AB| = 6\,\mathrm{cm}$. Calculate the area of the marked triangle if $E$ is the midpoint of the side $AB$.
$3\,\mathrm{cm}^2$
$6\,\mathrm{cm}^2$
$9\,\mathrm{cm}^2$
$12\,\mathrm{cm}^2$

9000046401

Level:
A
Consider the rectangle $ABCD$ with length and height $|AB| = 6\, \mathrm{cm}$ and $|BC| = 2\sqrt{3}\, \mathrm{cm}$, respectively. Find the measure of the angle $CAB$.
$30^{\circ }$
$45^{\circ }$
$60^{\circ }$

9000046402

Level:
A
Consider the rectangle $ABCD$ with length and height $|AB| = 6\, \mathrm{cm}$ and $|BC| = 2\sqrt{3}\, \mathrm{cm}$. Let $S$ be the intersection of diagonals. Find the angle $\measuredangle ASB$.
$120^{\circ }$
$60^{\circ }$
$90^{\circ }$