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- 1. Multiple Choice
When rectangle ABCD is reflected across line EF, the image is DCBA. How do you know that segment AB is congruent to segment DC?
A rectangle has 2 pairs of parallel sides.
Any 2 sides of a rectangle are congruent.
Congruent parts of congruent figures are corresponding.
Corresponding parts of congruent figures are congruent.
- 2. Multiple Choice
Select all statements that are true about the triangles.
Triangles ABC and DCB are congruent by the Angle-Angle Triangle Congruence Theorem.
Triangles ABC and BCD are congruent by the Angle-Side-Angle Triangle Congruence Theorem
Triangles ABC and BCD are congruent by the Side-Side-Side Triangle Congruence Theorem.
Triangles ABC and DCB are congruent by the Side-Angle-Side Triangle Congruence Theorem.
Triangles ABC and DCB are congruent by the Side-Side-Side Triangle Congruence Theorem.
- 3. Multiple Choice
Which sequence of rigid motions will definitely work to take triangle GHJ onto triangle STU?
Rotate GHJ using center G until GH is lined up with ST and then reflect over a line halfway between G'H'J' and STU.
Translate GHJ by the directed line segment GS. Rotate G'H'J' using S as the center by angle H'ST. Reflect G''H''J'' over ST.
Translate GHJ by the directed line segment GT. Rotate G'H'J' using T as the center by angle H'TS. Reflect G''H''J'' over ST.
Translate GHJ by the directed line segment GS.Translate G'H'J' by the directed line segment H'T. Translate G''H''J'' by the directed line segment J''T.
- 4. Multiple Choice
Reflect triangle STU across line ST. Which of these is a valid reason why the image of U will coincide with J?
The image of U and J are on the same side of ST and make the same angle with it at T.
The image of U and J are the same distance along the same ray from T.
The image of U and J will not coincide after reflection over ST.
Line ST is the perpendicular bisector of the segment connecting U and J, because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment.
- 5. Open Ended
Here is parallelogram ABCD. Prove segment AM is congruent to segment CM.
- 6. Open Ended
In parallelogram HIJK, the measure of angle H is 45 degrees. Find the measure of angle J. Explain how you know.
- 7. Open Ended
In parallelogram HIJK, the measure of angle H is 45 degrees. Find the measure of angle K. Explain how you know.
- 8. Fill in the Blank
The measure of angle Q is 70 degrees. Find the measure of angle P.
- 9. Open Ended
Use rigid motions to prove that figure ABC is congruent to figure EFG.
- 10. Multiple Choice
Triangle ABC is congruent to triangle EDF. So, Kiran knows that there is a sequence of rigid motions that takes ABC to EDF.
Angle B coincides with angle D.
Angle A coincides with angle F.
Segment AC coincides with segment EF.
Segment BC coincides with segment ED.
Segment AB coincides with segment ED.
- 11. Open Ended
What is the least amount of information that you need to construct a triangle congruent to this one?
- 12. Multiple Choice
Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of angle ABD.
147 degrees
136 degrees
138 degrees
151 degrees
- 13. Multiple Choice
Which triangle congruence theorem could you use to prove triangle ADE is congruent to triangle CBE?
Side-Angle-Side
Angle-Side-Angle
Side-Side-Angle
Side-Side-Side
- 14. Open Ended
Is triangle EJH congruent to triangle EIH? Explain your reasoning.
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