• 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.A.1
  

  Geometry

  7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

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• 7.G.A.2
  

  Geometry

  7.G.A.2 — Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

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Two triangles share two pairs of equal angles, as marked in the diagram. 
 

Mari thinks that $${\angle x}$$ and $${\angle y}$$ will always be equal, regardless of what the other angle measurements are. Do you agree with Mari’s reasoning? Why or why not?

Triangle $${{{ABC}}}$$ and triangle $${{AB'C'}}$$ share a common angle, $${\angle A}$$, and $${\overline{BC}}$$ is parallel to $${\overline{B'C'}}$$.

1. Is triangle $${{{ABC}}}$$ similar to triangle $${{AB'C'}}$$? Explain how you know. 
2. If the measure of $${\angle B}$$ is $${40^{\circ}}$$, then what is the measure of $${\angle C'}$$? Explain how you know. 
3. Draw a line in the diagram above that creates a new triangle that is similar to triangle $${{{ABC}}}$$.

Triangles $${ABC}$$ and $${PQR}$$ below share two pairs of congruent angles as marked:

1. Explain, using dilations, translations, reflections, and/or rotations, why $$\triangle {PQR}$$ is similar to $$\triangle {ABC}$$.
2. Are angles $$C$$ and $$R$$ congruent? Explain your reasoning.
3. Suppose $${{DEF}}$$ and $${{KLM}}$$ are two triangles with $${m(\angle D)=m(\angle K )}$$ and $${m(\angle E)=m(\angle L )}$$. Are triangles $${{DEF}}$$ and $${{KLM}}$$ similar?

Triangle $${{HIJ}}$$ and triangle $${{PQR}}$$ are shown below.

Are triangles $${{HIJ}}$$ and $${{PQR}}$$ similar? Justify your answer.