Lesson 21

One Hundred and Eighty

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Problem 1

The triangles here are each obtained by applying rigid motions to triangle 1. 

21 congruent triangle.
  1. Which triangles are translations of triangle 1? Explain how you know.
  2. 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.

A parallelogram with angle markings. Angle 1 in top left, Angle 2 in top right, 80 degrees in bottom left, and Angle 3 in bottom right.

Problem 3

In the figure shown, lines \(f\) and \(g\) are parallel. Select the angle that is congruent to angle 1.

Parallel lines f and g cut by a transversal, creating angles 1, 2, 3 and 4 at intersection of lines g and transversal, and creating angles 5, 6, 7 and 8 at intersection of lines f and transversal.
A:

Angle 2

B:

Angle 6

C:

Angle 7

D:

Angle 8

(From Geometry, Unit 1, Lesson 20.)

Problem 4

Angle \(BDE\) is congruent to angle \(BAC\). Name another pair of congruent angles. Explain how you know.  

Triangle and two horizontal line segments.
(From Geometry, Unit 1, Lesson 20.)

Problem 5

  1. Describe a transformation that could be used to show that corresponding angles are congruent.
  2. Describe a transformation that could be used to show that alternate interior angles are congruent.
(From Geometry, Unit 1, Lesson 20.)

Problem 6

Lines \(AD\) and \(EC\) meet at point \(B\).

Which of these must be true? Select all that apply. 

Lines AD and EC intersect at point B.
A:

A 180 degree clockwise rotation using center $B$ takes $D$ to $A$.

B:

The image of $D$ after a 180 degree rotation using center $B$ lies on ray $BA$.

C:

If a 180 degree rotation using center $B$ takes $C$ to $E$ then it also takes $E$ to $C$.

D:

Angle $ABC$ is congruent to angle $DBE$.

E:

Angle $ABE$ is congruent to angle $ABC$.

(From Geometry, Unit 1, Lesson 19.)

Problem 7

Points \(E\), \(B\), and \(C\) are collinear. Explain why points \(A\), \(B\), and \(D\) are collinear. 

Lines AD and EC intersect at point B. Angles ABE and CBD are 30 degrees.
(From Geometry, Unit 1, Lesson 19.)

Problem 8

  1. 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 \(CT\).
  2. Describe another sequence of transformations that will result in the same image.
     
A figure formed by 3 line segments, looks like the letter U. 4 points on the endpoints of the segments. Starting at the top left, A. Moving downard, C. Moving to the right, T. Moving upward, S.
(From Geometry, Unit 1, Lesson 18.)

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 \(C’\).

Two congruent triangles labeled ABC and A’B’C’.
(From Geometry, Unit 1, Lesson 17.)