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UNIT
14
14.3: Rotate a Figure
14
Trapezoid $$ABCD$$ is rotated $$90°$$ counterclockwise about $$O$$. Its image is the blue trapezoid $$A’B’C’D’$$. $$m \angle A$$ = $$90°$$, $$m \angle B$$ = $$135°$$, $$AB$$ = $$2 \;units$$, $$BC$$ = $$2.8 \;units$$, $$CD$$ = $$4\; units$$ and $$DA$$ = $$2\; units$$.

a) Label the vertices of the image
b) Give the length of its sides
c) Give the measure its angles

# Key Vocabulary

rotation
clockwise
counter
clockwise
angle
direction
congruent figures
orientation
image
preimage
center of rotation
360°
center of rotation
• To identify $$A’$$: Which vertex will make $$m \angle AOA’$$ = $$90°$$? Use the same way to determine $$B’,\; C’$$ and $$D’$$ $$(m \angle BOB’$$ = $$90°$$, $$m \angle COC’$$ = $$90°$$ and $$m \angle DOD’$$ = $$90°$$
• $$A’$$ is shown below.
• To find lengths of sides and measures: Since the $$2$$ trapezoids are identical (congruent), the length of the matching (corresponding) sides and angle measures are equal.
• $$AD\; =\; A’D’ ,\; m \angle A \;=\; m \angle A’$$