High school geometry

Answer all the questions below and press submit to see how many you got right.

id: 7924
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We look at a triangle with corners A,B and C. We call the sides opposite of A,B and C a, b and c and the midpoints of a,b,c D,E and F. Select all the statements that are true.

  • AD, BE and CF intersect in a point Z that cuts these line segments in the ratio 2:1.
    If AD and BE cross in X, AD and CF in Y and BE and CF in Z the XYZ is a right triangle.
    If AD, BE and CF intersect in a point Z, ABC is a right triangle.
    AD, BE and CF intersect in a point Z that cuts these line segments in the ratio 1:1.
id: 7754

Choose all statements that are true for an ellipse.

  • A circle is a special case of an ellipse
    The boundary of an ellipse is a set of points for which the distance from a point is constant.
    An ellipse is a special case of a circle
    The boundary of an ellipse is a set of points for which the combined distance from two points is constant.
id: 7931
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A quadrilateral ABCD is called cyclic if all of its points lie on a circle. Choose all statements that are true for a cyclic quadrilateral.

  • Opposite sides have the same lengths.
    ABCD is a rhombus.
    Opposite angles add up to $180^{\circ}.$
    The two diagonals of ABCD are perpendicular.