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Period: Date: $\newline$ $2$ . GIVEN: $\newline$ $ABCD$ is a rectangle PROVE: $\newline$ $\angle ADC \cong \angle BCD$

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Find the magnitude of a vector

Full solution

Q. Period: Date:

\newline

2

. GIVEN:

\newline

ABCD

is a rectangle PROVE:

\newline

\angle ADC \cong \angle BCD

Identify Properties: Identify the properties of a rectangle. In a rectangle, opposite sides are parallel and all angles are right angles ( $90^\circ$ ).
Angle Measurements: Since $ABCD$ is a rectangle, angle $ADC$ and angle $ABC$ are right angles. By definition, this means they both measure $90$ degrees.
Linear Pair Relationship: If angle $ADC$ is a right angle, then angle $BCD$ , which is adjacent to angle $ABC$ , must also be a right angle because they form a linear pair with angle $ABC$ and the sum of angles in a linear pair is $180$ degrees.
Congruent Right Angles: Since both angle $ADC$ and angle $BCD$ are right angles, they are congruent because all right angles are congruent.

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