Define and use the angle-angle criterion for similar triangles.
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In investigating the angle-angle criterion for similar triangles, students draw on concepts learned from throughout the unit, including rigid transformations, dilations, and the interior angle sum theorem. This lesson is a good opportunity to review these concepts from earlier in the unit.
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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 $${\overline{B'C'}}$$.
Triangles $${ABC}$$ and $${PQR}$$ below share two pairs of congruent angles as marked:
Similar Triangles II, accessed on Oct. 13, 2017, 4:25 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Modified by The Match Foundation, Inc.?
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Triangle $${{HIJ}}$$ and triangle $${{PQR}}$$ are shown below.
Are triangles $${{HIJ}}$$ and $${{PQR}}$$ similar? Justify your answer.
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