Lesson 21
One Hundred and Eighty
Problem 1
The triangles here are each obtained by applying rigid motions to triangle 1.
- Which triangles are translations of triangle 1? Explain how you know.
- Which triangles are not translations of triangle 1? Explain how you know.
Problem 2
The quadrilateral is a parallelogram. Find the measure of angles 1, 2, and 3.
Problem 3
In the figure shown, lines \(f\) and \(g\) are parallel. Select the angle that is congruent to angle 1.
Angle 2
Angle 6
Angle 7
Angle 8
Problem 4
Angle \(BDE\) is congruent to angle \(BAC\). Name another pair of congruent angles. Explain how you know.
Problem 5
- Describe a transformation that could be used to show that corresponding angles are congruent.
- Describe a transformation that could be used to show that alternate interior angles are congruent.
Problem 6
Lines \(AD\) and \(EC\) meet at point \(B\).
Which of these must be true? Select all that apply.
A 180 degree clockwise rotation using center $B$ takes $D$ to $A$.
The image of $D$ after a 180 degree rotation using center $B$ lies on ray $BA$.
If a 180 degree rotation using center $B$ takes $C$ to $E$ then it also takes $E$ to $C$.
Angle $ABC$ is congruent to angle $DBE$.
Angle $ABE$ is congruent to angle $ABC$.
Problem 7
Points \(E\), \(B\), and \(C\) are collinear. Explain why points \(A\), \(B\), and \(D\) are collinear.
Problem 8
- Draw the image of figure \(ACTS\) after a clockwise rotation around point \(C\) using angle \(CTS\) and then a translation by the directed line segment \(CT\).
- Describe another sequence of transformations that will result in the same image.
Problem 9
Triangle \(ABC\) is congruent to triangle \(A’B’C’\). Describe a sequence of rigid motions that takes \(A\) to \(A’\), \(B\) to \(B’\), and \(C\) to \(C’\).