Congruent Parts, Part 2

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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.68.G.A.2HSG-CO.B.8
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14 questions

Congruent Parts, Part 2

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Math Talk: Which Are Congruent?

Each pair of figures is congruent. Decide whether each congruence statement is true or false.

1) ABCFED\triangle ABC \cong \triangle FED.

Triangle ABCABC is congruent to triangle FEDFED.

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True or false? Write below.

2) PZJMLYXBPZJM \cong LYXB

Quadrilateral PZJMPZJM is congruent to quadrilateral LYXBLYXB.

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True or false? Write below.

3) JKLQRS\triangle JKL \cong \triangle QRS.

Triangle JKLJKL is congruent to triangle QRSQRS.

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True or false? Write below.

4) ABCDEPQRSTABCDE \cong PQRST

Pentagon ABCDEABCDE is congruent to pentagon PQRSTPQRST.

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True or false? Write below.
Which Triangles Are Congruent?

Here are three triangles.

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5) Triangle PQRPQR is congruent to which triangle?

6) Explain your reasoning.

7) Show a sequence of rigid transformations that takes PQRPQR to that triangle. Draw each step of the transformation.

8) Explain why there can’t be a rigid transformation to the other triangle.

Are These Parts Congruent?

9) Triangle ABDABD is a rotation of triangle CDBCDB around point EE by 180°180\degree.

Is angle ADBADB congruent to angle CDBCDB?

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True or false? Write below.

10) If so, explain your reasoning. If not, which angle is ADBADB congruent to?

11) Polygon HIJKLHIJKL is a reflection and translation of polygon GFONMGFONM.

Is segment KJKJ congruent to segment NMNM?

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True or false? Write below.

12) If so, explain your reasoning. If not, which segment is NMNM congruent to?

13) Quadrilateral PQRSPQRS is a rotation of polygon VZYWVZYW.

Is angle QRSQRS congruent to angle ZYWZYW?

True or false? Write below.

14) If so, explain your reasoning. If not, which angle is QRSQRS congruent to?