In the figure below, $AB$ is parallel to $CD$. $E, F$ are two points on $AB$ and $G, H$ ar

Question

In the figure below, $AB$ is parallel to $CD$. $E, F$ are two points on $AB$ and $G, H$ are two points on $CD$. Given that $EG, FH$ intersect at $M$ and the triangle $MGH$ is an isosceles triangle, where $MG = MH$. Find the sizes of angle $FEM$, angle $BEM$, angle $GMH$. Hence show that triangle $MFE$ is also an isosceles triangle.

Accepted Answer

(i) $41^\circ$ (ii) $139^\circ$ (iii) $98^\circ$ Hence $\triangle MFE$ is isosceles.

Angles Formed by Two Parallel Lines and a Transversal

Angles Formed by Two Parallel Lines and a Transversal

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