Independent Work Lesson 17: Transformations and Congruence Quiz

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'.

Answer: Translate quadrilateral ​ (a)    by the directed line segment ​ (b)   . Rotate the image using center ​ (c)   until the image of C ​ (d)   with C′.

• ABCD
• BB'
• B'
• coincides

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

(Two answers)

• Rotation of 180° around B

• Rotation of 180° around the midpoint of segment AB

• Reflection across the line AB

• Translation by the directed line segment AB

• Rotation of 180° around A

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'.

Answer: Translate triangle ​ (a)    by the directed line segment ​ (b)   . Rotate the image using center ​ (c)   until the image of B ​ (d)   with B′.

• ABC
• AA′
• A′
• coincides

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.

• It is a right triangle.

• All rotations take one half of the triangle to the other half of the triangle.

• None of the sides of the triangle have the same length.

• All angles of the triangle have the same measure.

Select all the angles of rotation that produce symmetry for this flower. (Hint 2 choices).

• 60

• 120

• 30

• 90

• 180

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

• C. Two sides of the triangle have the same length.

• D. Two angles of the triangle have the same measure.

• A. All sides of the triangle have the same length.

• E. No sides of the triangle have the same length.

• B. All angles of the triangle have the same measure.

In quadrilateral BADC, AB = AD and BC = DC. The line AC is a line of symmetry for this quadrilateral. Based on the line of symmetry, why do angles ACB and ACD have the same measure?

• A. Because AB = AD and BC = DC.

• B. Because AC is a line of symmetry.

• C. Because angles ACB and ACD are opposite angles.

• D. Because angles ACB and ACD are complementary.

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

• A. Construct the midpoint of segment AB.

• B. Construct the perpendicular bisector of segment AB.

• C. Construct a line tangent to circle A with radius AB.

• D. Construct a vertical line passing through point A and a horizontal line passing through point B.