Geometry: Triangle ABC and Quadrilateral ADFE

Geometry vocabulary and key concepts derived from a lecture transcript involving triangle proofs, midpoints, and quadrilateral classification.

Right-angled triangle ($\Delta ABC$)

A triangle where the angle at vertex $A$ is given as $90^{\circ}$.

Midpoint ($D$)

A point on line segment $AB$ that divides the segment into two equal parts.

Parallel ($\parallel$)

A relationship between line segments, specifically $DE \parallel BC$ and $FD \parallel AB$, where they remain equidistant and never intersect.

$$AE = EC$$

A property to be proven in $\Delta ABC$ demonstrating that $E$ is the midpoint of side $AC$ given $D$ is the midpoint and $DE \parallel BC$.

Perpendicular ($\perp$)

A relationship where two lines intersect at a right angle ($90^{\circ}$), such as the given condition $AB \perp EF$.

$$\hat{E}_1 = 30^{\circ}$$

The specific angular measure provided to help determine the type of quadrilateral formed by vertices $A$, $D$, $F$, and $E$.

Quadrilateral $ADFE$

A four-sided polygon defined by points $A$, $D$, $F$, and $E$ whose specific classification is calculated based on its geometric properties.

$$FD \parallel AB$$

A given geometric condition where the line segment $FD$ is parallel to the side $AB$ of the triangle.