Unit 1, Lesson 17

Working with Rigid Transformations

Geometry

Practice

Problem 1

Quadrilateral is congruent to quadrilateral . Describe a sequence of rigid motions that takes to , to , to , and to .

<p>Congruent quadrilaterals A B C D and A prime B prime C prime D prime. </p>

Practice

Problem 2

Select all transformations that must take any point to any point .

Rotation of around

Problem 3

Triangle is congruent to triangle . Describe a sequence of rigid motions that takes to , to , and to .

<p>Congruent triangles A B C and A prime B prime C prime.</p>

Problem 4

ForLesson 16: More Symmetry

A triangle has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this.

All sides of the triangle have the same length.
All angles of the triangle have the same measure.
All rotations take one half of the triangle to the other half of the triangle.
It is a right triangle.
None of the sides of the triangle have the same length.
None of the angles of the triangle have the same measure.

Problem 5

ForLesson 16: More Symmetry

Select all the angles of rotation that produce symmetry for this flower.

Problem 6

ForLesson 15: Symmetry

A right triangle has a line of symmetry. Select all conclusions that must be true.

All sides of the triangle have the same length.
All angles of the triangle have the same measure.
Two sides of the triangle have the same length.
Two angles of the triangle have the same measure.
No sides of the triangle have the same length.
No angles of the triangle have the same measure.

Problem 7

ForLesson 15: Symmetry

In quadrilateral , and . The line is a line of symmetry for this quadrilateral. Based on the line of symmetry, explain why angles and have the same measure.

Problem 8

ForLesson 11: Defining Reflections

Which of these constructions would construct a line of reflection that takes the point to point ?

Construct the midpoint of segment .

Problem 9

ForLesson 13: Incorporating Rotations

Here is triangle . Match the description of the rotation with the image of after that rotation.

<p>Triangle P O G on isometric grid. P O and O G are both 2 units long. O G is vertical.</p>

Rotate 300 degrees clockwise around .
Rotate 60 degrees clockwise around .

Rotation of around

Rotation of around the midpoint of segment

Reflection across the line

Reflection across the perpendicular bisector of segment

Translation by the directed line segment

Construct the perpendicular bisector of segment .

Construct a line tangent to circle with radius .

Construct a vertical line passing through point and a horizontal line passing through point .

Rotate 60 degrees clockwise around .

Rotate 240 degrees counterclockwise around .

Triangle P prime O prime G prime on an isometric grid. Point O prime faces upwards and to the right, P prime faces downwards, G prime faces upwards and to the left.
Triangle P prime O prime G prime on an isometric grid. Point O prime faces downwards and to the left, P prime faces upwards, G prime faces downwards and to the right.

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Working with Rigid Transformations

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9