Congruent Parts, Part 1

ID: tubon-logig
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
Standards: HSG-CO.B.7HSG-CO.B.6HSG-CO.A.58.G.A.1HSG-CO.C.11
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12 questions

Congruent Parts, Part 1

Classroom:
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Notice and Wonder: Transformed Rectangles

1) What do you notice? What do you wonder?

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If We Know This, Then We Know That...

Triangle ABCABC is congruent to triangle DEFDEF.

ABCDEF\triangle ABC \cong \triangle DEF

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2) Find a sequence of rigid motions that takes triangle ABCABC to triangle DEFDEF.

3) What is the image of segment BCBC after that transformation?

4) Explain how you know those segments are congruent.

5) Justify that angle ABCABC is congruent to angle DEFDEF.

Making Quadrilaterals

6) Draw a triangle.

7) Find the midpoint of the longest side of your triangle.

8) Rotate your triangle 180°180 \degree using the midpoint of the longest side as the center of the rotation.

9) Label the corresponding\textbf{corresponding} parts and mark what must be congruent.

Make a conjecture and justify it.

10) What type of quadrilateral have you formed?

11) What is the definition of that quadrilateral type?

12) Why must the quadrilateral you have fit the definition?