In Exercises 39 and 40, complete each proof. Given: Plane M C is the midpoint of E B A D ⊥B E

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In Exercises 39 and 40, complete each proof. Given: Plane...

In Exercises 39 and $40,$ complete each proof.
Given: $\quad$ Plane $M$
$C$ is the midpoint of $\overline{E B}$
$\overline{A D} \perp \overline{B E}$ and $\overline{A B} \| \overline{E D}$
Prove:
$\triangle A B C \equiv \triangle D E C$
(GRAPH CANT COPY)

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Key Concepts

Midpoint

A midpoint is the point that divides a line segment into two congruent segments. In geometric proofs, establishing that a point is the midpoint can provide the information that two segments are equal, which is often a crucial step in proving congruence or symmetry between parts of a figure.

Triangle Congruence

Triangle congruence involves proving that two triangles have exactly the same size and shape by showing that corresponding sides and angles are equal. Common congruence criteria, such as ASA (angle?side?angle) or SAS (side?angle?side), are used to establish that if certain sets of sides and angles are equal, then all parts of the triangles are congruent.

Parallel Lines and Angle Relationships

Parallel lines have a unique property that when they are intersected by a transversal, corresponding angles and alternate interior angles are congruent. This property allows for the establishment of equal angles in geometric figures, which is frequently used to prove triangle congruence.

Perpendicular Lines

Perpendicular lines intersect to form right angles (each measuring 90 degrees). This relationship is critical in geometric proofs because right angles serve as a fixed reference for angle measures, facilitating the demonstration of similarity or congruence between different geometric components.

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