Polygons

1003021307

Level:

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:

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) \cdot 180^{\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.

1003085406

Level:

A diagonal of a rectangle has length of

30 cm

and the perimeter of the rectangle is

84 cm

. Find the difference of the length and the width of the rectangle in centimeters.

6

8

9

10

1103021301

Level:

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:

The aspect ratio of the sides of the

A B C D

rectangle is

\sqrt{3} : 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 rectangle with sides

a

b

is given. The angle between diagonals

α = 60^{\circ}

. The longer side

a = 6 cm

. Calculate the length of the shorter side

b

\frac{6}{\sqrt{3}} cm

\frac{3}{\sqrt{3}} cm

\frac{1}{\sqrt{3}} cm

6 \sqrt{3} cm

1103021304

Level:

The side lengths of the rectangle

A B C D

are in the ratio

A B : B C = 12 : 5

. Give the degree measure of the angle

C A B

. Round the result to two decimal places.

{22.62}^{\circ}

{67.38}^{\circ}

{24.62}^{\circ}

{65.38}^{\circ}

1103021305

Level:

A B C D

is a square. Determine the degree measure of the angle

E G D

if the measure of the angle

C F G

50^{\circ}

5^{\circ}

10^{\circ}

15^{\circ}

20^{\circ}

1103021306

Level:

In the square

A B C D

| A B | = 6 cm

. Calculate the area of the marked triangle if

E

is the midpoint of the side

A B

3 {cm}^{2}

6 {cm}^{2}

9 {cm}^{2}

12 {cm}^{2}

2000005501

Level:

Derive the formula for the area of a square using the length of its diagonal

u

\frac{u^{2}}{2}

4 u^{2}

\frac{u^{2}}{4}

2 u^{2}

1003021307

1003021308

1003085406

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1103021302

1103021303

1103021304

1103021305

1103021306

2000005501

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