High school geometry

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

id: 7756

Choose all statements that are true.

  • The set of points $\{(x,y)| \frac{x^2}{2}+\frac{y^2}{2}=D \}$ is the boundary of a circle with diameter $D.$
    The set of points $\{(x,y)| x^2+y^2=R^2 \}$ is the boundary of a circle with radius $R.$
    The set of points $\{(x,y)| \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \}$ is the boundary of an ellipse.
    The set of points $\{(x,y)| x^2+y^2=R \}$ is the boundary of a circle with radius $R.$
id: 7933
Card image cap

A line crosses the center of a circle and crosses the circle in points A and B. We pick any point C on the circle not equal to A or B. Choose all the statements about the triangle ABC that are true.

  • The angle at C is a right angle.
    The height of the triangle perpendicular to AB is independent of the location of C.
    The angles at A and B add up to $90^{\circ}.$
    The area of the triangle is independent of the location of C.
id: 7922
Card image cap

Choose all statements that are true for a rhombus.

  • Angles at opposite corners are the same.
    Angles at adjacent corners add up to $180^{\circ}$
    It has two pairs of parallel sides all of which have the same length.
    All of its angles are acute.