standard_description: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
problem_activity: Task
In triangles $ABC$ and $DEF$ below $m(\angle A) = m(\angle D)$, $m(\angle B) = m(\angle E)$ and $|\overline{AB}| = |\overline{DE}|$.
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Find a sequence of translations, rotations, and reflections which maps $\triangle ABC$ to $\triangle DEF$.
After working on problem (a), Melissa says
Since $m(\angle A) = m(\angle D)$ and $m(\angle B) = m(\angle E)$ then I also know that $m(\angle C) = m(\angle F)$. So these triangles share all three angles and this is enough to know that they are congruent. I don't need to be told that $|\overline{AB}| = |\overline{DE}|$.
Is Melissa correct that $m(\angle C) = m(\angle F)$? Explain.
Is she right that two triangles sharing three pairs of congruent angles are always congruent? Explain.
Below are two triangles which share three congruent angles: $m(\angle P) = m(\angle T)$, $m(\angle Q) = m(\angle U)$, $m(\angle R) = m(\angle V)$:
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Show that, after applying a suitable dilation, $\triangle PQR$ is congruent to $\triangle TUV$.


aligns: no