cmi-entrance 2023 QA2

cmi-entrance · India · ugmath 4 marks Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane
Suppose a rectangle $EBFD$ is given and a rhombus $ABCD$ is inscribed in it so that the point $A$ is on side $ED$ of the rectangle. The diagonals of $ABCD$ intersect at point $G$.
Statements
(5) Triangles $CGD$ and $DFB$ must be similar. (6) It must be true that $\frac { AC } { BD } = \frac { EB } { ED }$. (7) Triangle $CGD$ cannot be similar to triangle $AEB$. (8) For any given rectangle $EBFD$, a rhombus $ABCD$ as described above can be constructed.
Suppose a rectangle $EBFD$ is given and a rhombus $ABCD$ is inscribed in it so that the point $A$ is on side $ED$ of the rectangle. The diagonals of $ABCD$ intersect at point $G$.

\textbf{Statements}

(5) Triangles $CGD$ and $DFB$ must be similar.\\
(6) It must be true that $\frac { AC } { BD } = \frac { EB } { ED }$.\\
(7) Triangle $CGD$ cannot be similar to triangle $AEB$.\\
(8) For any given rectangle $EBFD$, a rhombus $ABCD$ as described above can be constructed.