Lesson 17

Quadrilateral \(ABCD\) is congruent to quadrilateral \(A’B’C’D’\). Describe a sequence of rigid motions that takes \(A\) to \(A’\), \(B\) to \(B’\), \(C\) to \(C’\), and \(D\) to \(D’\).

Select all transformations that must take any point \(A\) to any point \(B\).

Rotation of \(180^\circ\)around \(A\)

Rotation of \(180^\circ\)around \(B\)

Rotation of \(180^\circ\)around the midpoint of segment \(AB\)

Reflection across the line \(AB\)

Reflection across the perpendicular bisector of segment \(AB\)

Translation by the directed line segment \(AB\)

Translation by the directed line segment \(BA\)

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.

30

45

60

90

120

135

180

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.

Which of these constructions would construct a line of reflection that takes the point \(A\) to point \(B\)?

Construct the midpoint of segment \(AB\).

Construct the perpendicular bisector of segment \(AB\).

Construct a line tangent to circle \(A\) with radius \(AB\).

Construct a vertical line passing through point \(A\) and a horizontal line passing through point \(B\).