Congruence and Similarity

• Left 6, up 5

• Left 6, down 5

• Right 6, up 5

• Right 6, down 5

Describe the transformation that maps RSTU onto R'S'T'U'.

• Reflect over x = 1 and translate 2 units down.

• Translate 8 units right and 2 units up.

• Reflect over x = 1 and translate 2 units up.

• Translate 8 units left and 2 units down.

Which two figures are congruent?

• Figures A and B

• Figures A and C

• Figures A and D

• Figures C and D

• Yes. A dilation with center (0,0) and a scale factor of 1/2 maps ABC to ADE.

• Yes. A dilation with center (0,0) and a scale factor of 2 maps ABC to ADE.

• Yes. A translation 2 units up and 4 units right maps ADE to ABC.

• No. ABC is not similar to ADE.

Match the congruent sides and angles.

• BC

• AC

• < F

• < B

• DE

• < A

• < E

• DF

• < C

• < D

• Reflection across the x-axis, translation down 4 and right 1.

• Rotation 180° about the origin, translation down 1 and right 2.

• Rotation 180° about the origin, translation down 2 and right 2.

• Reflection across the x-axis, down 6 and right 3.

• m∠1 = m∠6

• m∠2 = m∠6

• m∠1 + m∠6 = 180°

• x = 90°

• x = 120°

• (4, -3)

• (-6, 1)

• (4, 0)

• (-2, 1)

Describe the sequence of transformations that maps Figure A to Figure C.

• Rotate Figure A 180º and then translate it 1 unit left.

• Rotate Figure A 90º and then reflect it over the x-axis.

• Rotate Figure A 90º, reflect if over the x-axis, and then translate it 1 unit down and 1 unit to the left.

• Rotate Figure A 180º and then translate it 1 unit down and 1 unit to the left.

• ∠1 = 30°, m∠2 = 35°

• ∠1 = 35°, m∠2 = 30°

• ∠1 = 65°, m∠2 = 60°

• ∠1 = 85°, m∠2 = 80°