Lesson 10

Rigid Transformations

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Problem 1

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

A:
Congruent triangles A B C and A prime B prime C prime.
B:
Congruent triangles A B C and A prime B prime C prime.
C:
Congruent triangles A B C and A prime B prime C prime.
D:
Triangles A B C and A prime B prime C prime. Triangle A B C is smaller.

Solution

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Problem 2

What is the definition of congruence?

A:

If two figures have the same shape, then they are congruent.

B:

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.

D:

If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.

Solution

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Problem 3

There is a sequence of rigid transformations that takes \(A\) to \(A’\), \(B\) to \(B’\), and \(C\) to \(C’\). The same sequence takes \(D\) to \(D’\). Draw and label \(D’\):

Triangles A B C and A prime B prime C prime. Point D is located on side B C.

Solution

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Problem 4

Three schools are located at points \(A\), \(B\), and \(C\). 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? Explain or show your reasoning.

A square with 3 points inside. Point A is in the upper left. Point B is in the bottom left. Point C is near the middle right.

Solution

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(From Unit 1, Lesson 9.)

Problem 5

To construct a line passing through point \(C\) that is parallel to the line \(AB\), Han constructed the perpendicular bisector of \(AB\) and then drew line \(CD\).

Overlapping circles with centers A and B. Vertical line through intersection points. 1 intersection point labeled D. Horizontal line through AB and horizontal line through D with point C on it.

Is \(CD\) guaranteed to be parallel to \(AB\)? Explain how you know.

Solution

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(From Unit 1, Lesson 6.)

Problem 6

This diagram is a straightedge and compass construction of a line perpendicular to line \(AB\) passing through point \(C\). Select all the statements that must be true.

Three circles.
A:

\(AD=BD\)

B:

\(EC=AD\)

C:

\(AC=DC\)

D:

\(EA=ED\)

E:

\(ED=DB\)

F:

\(CB=AD\)

Solution

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(From Unit 1, Lesson 5.)