Rigid Transformations

ID: rakaz-panul
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Rigid Transformations

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Problem 1

1) Here are 4 triangles that have each been transformed by a different transformation. Which figure shows a transformation that is not a rigid transformation?

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a) Figure A\text{Figure A}b) Figure B\text{Figure B}c) Figure C\text{Figure C}d) Figure D\text{Figure D}
Problem 2

2) What is the definition of congruence?

a) If two figures have the same shape, then they are congruent. \text{If two figures have the same shape, then they are congruent. }b) If two figures have the same area, then they are congruent. \text{If two figures have the same area, then they are congruent. }c) If there is a sequence of transformations taking one figure to another, then they are congruent. \text{If there is a sequence of transformations taking one figure to another, then they are congruent. }d) If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.\text{If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.}
Problem 3

3) There is a sequence of rigid transformations that takes AA to AA', BB to BB', and CC to CC'. The same sequence takes DD to DD'. Draw and label DD':

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Problem 4

4) Three schools are located at points AA, BB, and CC. The school district wants to locate its new stadium at a location that will be roughly the same distance from all 3 schools. Where should they build the stadium?

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5) Explain or show your reasoning.

Problem 5

6) To construct a line passing through point CC that is parallel to the line ABAB, Han constructed the perpendicular bisector of ABAB and then drew line CDCD.

Is CDCD guaranteed to be parallel to ABAB?

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True or false? Write below.

7) Explain how you know.

Problem 6

8) This diagram is a straightedge and compass construction of a line perpendicular to line ABAB passing through point CC. Select all the statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) AD=BDAD=BD \quad\quad b) EC=ADEC=AD \quad\quad c) AC=DCAC=DC \quad\quad d) EA=EDEA=ED \quad\quad e) ED=DBED=DB \quad\quad f) CB=ADCB=AD

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