Mid-Point Theorem

Use mid-segment theorem to name a segment that has twice the length of $\mathrm{EC}: \left(\mathrm{AD}/\mathrm{DE}/\mathrm{BC}/\mathrm{AC}\right)$

Use mid-segment theorem to name the part of the given triangle: A segment that has half the length of $AC$. $(\mathrm{BD} / \mathrm{BE} / \mathrm{DE})$

Use mid-segment theorem to name the part of the given triangle: A segment that has the same length as $\mathrm{BD}$.

Use mid-segment theorem to name the part of the given triangle: A segment parallel to $\mathrm{AC}$. $\left(\mathrm{AB}/\mathrm{AC}/\mathrm{BC}\right)$

Use mid-segment theorem to name the part of the given triangle: A mid-segment of $\Delta \mathrm{ABC}$. $\left(\mathrm{AB}/\mathrm{BC}/\mathrm{AC}/\mathrm{DE}\right)$

Find the measure of $NZ$:

The measure of $XZ$ is $y \mathrm{cm}$. Find the value of $y$.

The measure of $\mathrm{NM}$ is $x \mathrm{cm}$. Find the value of $x$.

In the figure given below, $E$ is the midpoint of side $AD$ of a trapezium $ABCD$ with $AB\Vert DC.$ A line through $E$ parallel to $AB$, meets $BC$ in $F$. Show that $F$ is the midpoint of $BC$.

Prove that in a parallelogram, the lines joining a pair of opposite vertices to the mid-points of a pair of opposite sides trisect a diagonal.

$ABCD$ is a parallelogram, $E$ is the midpoint of $AB$ and $F$ is the midpoint of $CD$. $GH$ is any line that intersects $AD, EF$ and $BC$ in $G, P$ and $H$ respectively. Prove that $GP=PH$.

In the quadrilateral $ABCD$ the midpoints of $AB, BC, CD, DA$ are $L, M, P, Q$. If it is also given that the diagonals $AC$ and $BD$ are equal. What further statement can be made about the parallelogram $LMPQ$?

In the quadrilateral $ABCD$, the midpoints of $AB, BC, CD, DA$ are $L, M, P, Q$. Prove that $LMPQ$ is a parallelogram.

In the quadrilateral $ABCD$, the midpoints of $AB, BC, CD, DA$ are $L, M, P, Q$. Using the midpoint theorem make a statement concerning the lengths and directions of $LM$ and $AC$.

A quadrilateral $ABCD$ is a rhombus and $P, Q, R, S$ are the midpoints of $AB, BC, CD, DA$ respectively. Prove that quad. $PQRS$ is a rectangle.

Show that the quadrilateral, formed by joining the midpoints of the consecutive sides of a rectangle, is a rhombus.