Section D Section D Checkpoint

Problem 1

Line FGFG is parallel to line HJHJ and cut by transversal mm. Find each angle measure:

  1. aa
  2. bb
  3. cc
  4. dd
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Solution
  1. 45∘45^\circ
  2. 135∘135^\circ
  3. 45∘45^\circ
  4. 135∘135^\circ
Show Sample Response
Sample Response
  1. 45∘45^\circ
  2. 135∘135^\circ
  3. 45∘45^\circ
  4. 135∘135^\circ

Problem 2

Line ABAB is parallel to line CDCD. Explain how you know that the sum of the angles of triangle ABCABC is 180∘180^\circ.

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Solution
Sample response: Angles ECAECA, ACBACB, and BCDBCD form a straight angle, which is 180∘180^\circ. Angle ECAECA is congruent to angle CABCAB because they are alternate interior angles. Angle BCDBCD is congruent to angle CBACBA because they are alternate interior angles. So the angles in triangle ABCABC are congruent to the angles that make a straight angle and must also sum to 180∘180^\circ.
Show Sample Response
Sample Response
Sample response: Angles ECAECA, ACBACB, and BCDBCD form a straight angle, which is 180∘180^\circ. Angle ECAECA is congruent to angle CABCAB because they are alternate interior angles. Angle BCDBCD is congruent to angle CBACBA because they are alternate interior angles. So the angles in triangle ABCABC are congruent to the angles that make a straight angle and must also sum to 180∘180^\circ.