幾何與角

In the figure, $ABCD$ is a parallelogram. $E$ is the mid-point of $AB$. $F$ and $G$ are points lying on $CD$ such that $DF=FG=GC$. $BG$ and $CE$ intersect at $H$. If the area of $\triangle BCH$ is $6\text{ cm}^2$, then the area of the quadrilateral $EFGH$ is

In the figure, $D$ is a point lying on $AB$ such that $AD=BD=CD$. Find $x+y$.

If the plane figure above is rotated anticlockwise about the point $O$ through $270^\circ$, which of the following is its image?

In the figure, the rhombus $ABCD$ is divided into sixteen identical rhombuses and six of them are shaded. The number of axes of reflectional symmetry of the rhombus $ABCD$ is

In the figure, $BED$ is a diagonal of the parallelogram $ABCD$. If $\angle DCE=20^\circ$, $\angle AED=130^\circ$ and $CE=DE$, then $\angle BAE=$

If the sum of the exterior angles of a regular $n$-sided polygon is $3$ times an interior angle of the polygon, then $n=$

The coordinates of the point $A$ are $(-3,2)$. If $A$ is translated downwards by $7$ units to the point $B$, then the coordinates of the reflection image of $B$ with respect to the straight line $x=1$ are

In the figure, $ABCDE$ is a circle. $AC$ and $BD$ intersect at $F$. If $AE\parallel BD$, $\angle DAE=20^\circ$ and $\angle CFD=70^\circ$, then $\angle CBD=$

In the figure, $BC$ is a diameter of the circle $ABC$. $BCD$ is a straight line and $DA$ is the tangent to the circle at $A$. If $\angle ABC=28^\circ$, then $\angle ADB=$

Which of the following statements about a cube must be true? I. The number of planes of reflection is $9$. II. All the axes of rotational symmetry intersect at the same point. III. The angle between any two intersecting axes of rotational symmetry is $90^\circ$.