• 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
  

  Geometry

  8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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• 8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
  

  Geometry

  8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

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• 7.G.B.5
  

  Geometry

  7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

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Suppose $$l$$ and $$m$$ are parallel lines, with $$Q$$ a point on $$l$$ and $$P$$ a point on $$m$$, as pictured below. Also labeled in  the picture is point $$M$$, the midpoint of $$\overline{PQ}$$, and two angles $$a$$ and $$b$$.

How can you use a rotation to prove that angles $$a$$ and $$b$$ are congruent?

In the picture below, $$m$$ and $$n$$ are parallel lines and angles $$a$$ and $$b$$ are shown. Show that angle $$a$$ is congruent to angle $$b$$ using rigid motions.

In the diagrams below, lines $$b$$ and $$c$$ are parallel; lines $$f$$ and $$d$$ are not parallel.

1. Identify all of the angles congruent to $${{\angle 1}}$$ in the first diagram. Explain why each angle is congruent to $${{\angle 1}}$$.
2. Identify all of the angles congruent to $${{\angle 1}}0$$ in the second diagram. Explain why each angle is congruent to $${{\angle 1}}0$$.

Use the diagram to answer the two questions that follow. In the diagram, lines $${{{L_1}}}$$ and $${{{L_2}}}$$ are intersected by transveral $$m$$, forming angles 1-8, as shown.

1. If $${{{L_1}}}$$ and $${{{L_2}}}$$ are parallel, what do you know about $${\angle 2}$$ and $${\angle 6}$$? Use informal arguments to support your claim.
2. If $${{{L_1}}}$$ and $${{{L_2}}}$$ are parallel, what do you know about $${\angle 1}$$ and $${\angle 3}$$? Use informal arguments to support your claim.