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9-12 Integrated Math 1 Unit 1 Lesson 10

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K-5 Math 6-8 Math •9-12 Math

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•Integrated Math 1

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 •Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19

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9-12

Integrated Math 1

Algebra 1

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Unit 1, Lesson 10

Rigid Transformations

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Integrated Math 1

Practice

Problem 1

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

Problem 2

What is the definition of congruence?

If two figures have the same shape, then they are congruent.
If two figures have the same area, then they are congruent.
If there is a sequence of transformations taking one figure to another, then they are congruent.
If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.

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 \(D’\):

<p>Triangles A B C and A prime B prime C prime. Point D is located on side B C.</p>

Problem 4

ForLesson 9: Speedy Delivery

Three schools are located at points \(A\), \(B\), and \(C\). The school district wants to build 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.

<p>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.</p>

Problem 5

ForLesson 6: Construction Techniques 4: Parallel and Perpendicular Lines

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 \(CD\).

<p>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.</p>

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

Problem 6

ForLesson 5: Construction Techniques 3: Perpendicular Lines and Angle Bisectors

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.

<p>Three circles.</p>

\(AD=BD\)
\(EC=AD\)
\(AC=DC\)
\(EA=ED\)
\(ED=DB\)
\(CB=AD\)