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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.
  • \(AD\; =\; A’D’ ,\; m \angle A \;=\; m \angle A’\)