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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
Triangle HEF is the image of triangle FGH after a 180 degree rotation about point K. Select all statements that must be true.
Angle FEH is congruent to angle FGH
EFGH is a rhombus.
Diagonal FH bisects angles EFG and EHG
Diagonal FH is perpendicular to side FE
Angle EHF is congruent to angle FGH
- 3. 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.
Select all true statements after the transformations:
Angle A coincides with angle F
Angle B coincides with angle D.
Segment AC coincides with segment EF.
Segment BC coincides with segment ED.
Segment AB coincides with segment ED.
- 4. Multiple Choice
The triangles are congruent. Which sequence of rigid motions will take triangle XYZ onto triangle BCA?
Translate XYZ using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with B. Reflect X"Y"Z" across line CB
Translate XYZ using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with B. Reflect X"Y"Z" across line AC.
Translate XYZ using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with A. Reflect X"Y"Z" across line CB.
Translate XYA using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with A. Reflect X"Y"Z across line AC.
- 5. Multiple Choice
Triangle ABC is congruent to triangle DEF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent.
Segment AC is congruent to segment EF
Segment BC is congruent to segment EF
Angle BAC is congruent to angle EDF
Angle BCA is congruent to angle EDF
Angle CBA is congruent to angle DEF
- 6. Multiple Choice
When triangle ABC is reflect across line AB, the image is triangle ABD. Why is angle ACD congruent to angle ADB?
Corresponding parts of congruent figures are congruent.
Congruent parts of congruent figures are corresponding.
Segment AB is perpendicular bisector of segment DC
An isosceles triangle has a pair of congruent angles
- 7. Multiple Choice
When rectangle ABCD is reflected across line EF, the image is BADC.
How do you know that segment AD is congruent to segment BC?
A rectangle has pairs of parallel sides.
Any 2 sides of a rectangle are congruent.
Corresponding parts of congruent figures are congruent.
Congruent parts of congruent figures are corresponding.
- 8. Multiple Choice
Write a sequence of rigid motions to take figure ABC to figure DEF.
Rotate figure ABC using B as the center. Translate figure ABC by the directed line segment from C to F so that the image of C coincides with F.
Translate figure ABC by the directed line segment from C to F . Rotate the image of figure ABC using F as the center so that the image of B coincides with E.
Translate figure ABC by the directed line segment from C to F. Reflect figure ABC over line segment FE so that the image of A coincides with D.
Reflect figure ABC over line segment FE so that the image of A coincides with D. Rotate figure ABC using B as the center.
- 9. Multiple Choice
Triangle DAC is isosceles with congruent sides AD and AC. Which additional given information is sufficient for showing that triangle DBC is isosceles? Select all that apply.
Line AB is an angle bisector of DAC
Angle BAD is congruent to angle ABC.
Angle BDC is congruent to angle BCD.
Angle ABD is congruent to angle ABC.
Triangle DAB is congruent to triangle CAB
- 10. Fill in the Blank
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.
- 11. Multiple Choice
What triangle congruence theorem could you use to prove triangle ADE is congruent to triangle CDE?
Side-Angle-Side Triangle Congruence
Angle-Side-Angle Triangle Congruence
Side-Side-SIde Triangle Congruence
Side-Side-Angle Triangle Congruences
- 12. Multiple Choice
Each statement is always true. Select all statements for which the converse is also always true.
Statement: If 2 angles are vertical, then they are congruent.
Converse: If 2 angles are congruent, then they are vertical.
Statement: If 2 lines are perpendicular, then they intersect to form 4 right angles.
Converse: If 2 lines intersect to form 4 right angles, then they are perpendicular.
Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment.
Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.
Statement: In an isosceles triangle, the base angles are congruent.
Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.
Statement: If 2 angles form a straight angle, then they are supplementary.
Converse: If 2 angles are supplementary, then they form a straight angle.
- 13. Multiple Choice
In isosceles triangle DAC, AD is congruent to AC. Karl knows that the base angles of an isosceles triangle are congruent. Select all the choices that would allow Karl to show that AB is a perpendicular bisector of segment CD.
AB is an angle bisector.
DB is congruent to BC.
AB is congruent to itself.
AB is perpendicular to DC.
Angle ABD is congruent to angle ABC.
- 14. Multiple Choice
Triangle DAC is isosceles.
What information do you need to show that triangle DBA is congruent to triangle CBA by the Side-Angle-Side Triangle Congruence Theorem?
DC is congruent to itself.
Angle ABD is congruent to angle BAC.
Angle BAD is congruent to angle BCA.
Angle BAD is congruent to angle BAC.
- 15. Multiple Choice
Refer to the figures.
Which of the following is a sequence of rigid motions to take figure CBA to figure MLK?
Translate figure ABC by the directed line segment from B to L. Rotate the image of figure ABC using M as the center so that the image of A coincides with M.
Translate figure ABC by the directed line segment from C to M. Rotate the image of figure ABC using M as the center so that the image of B coincides with L.
Reflect figure ABC across segment CL. Reflect the image of figure ABC across segment BL.
There isn't a sequence of rigid motions to take figure CBA to figure MLK.
- 16. Fill in the Blank
WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZWX has a measure of 60 degrees. Find the measure of angle ZYW.
Angle ZYW has a measure of ______ degrees.
- 17. Multiple Choice
Select all true statements based on the diagram.
Angle CBE is congruent to angle ABE
Angle CEB is congruent to angle DEA
Segment DA is congruent to segment CB
Segment DC is congruent to segment AB
- 18. Multiple Choice
Select all true statements based on the diagram.
Angle CBE is congruent to angle DEA
Angle CEB is congruent to angle DEA
Segment DA is congruent to segment CB
Segment DC is congruent to segment AB
Line DC is parallel to line AB
- 19. Multiple Choice
The triangles are congruent. Which sequence of rigid motions takes triangle DEF onto triangle DEF onto triangle BAC.
Translate DEF using directed line segment. EA. Rotate D'E'F' using A as the center so that D' coincides with C. Reflect D"E"F" across line AC
Translate DEF using directed line segment EA. Rotate D'E'F' using A as the center so that D' coincides with C. Reflect D"E"F" across line AB.
Translate DEF using directed line segment EA. Rotate D'E'F' using A as the center so that D' coincides with B. Reflect D"E"F across line AC.
Translate DEF using directed line segment EA. Rotate D'E'F' using A as the center so that D' coincides with B. Reflect D"E"F across line AB.
- 20. Multiple Choice
Lin is using the diagram to prove the statement, "If a parallelogram has one right angle, it is a rectangle." Given that EFGH is a parallelogram and angle HEF is right, which reasoning about angles will help her prove that angle FGH is also a right angle?
Corresponding angles are congruent when parallel lines are cut by a transversal.
Opposite angles in a parallelogram are congruent.
Vertical angles are congruent.
The base angles of an isosceles triangles are congruent.
- 21. Multiple Choice
What conjecture is possible to prove?
If the four angles in a quadrilateral are congruent to the four angles in another quadrilateral, then the two quadrilaterals are congruent.
If the four sides in a quadrilateral are congruent to the four sides in another quadrilateral, then the two quadrilaterals are congruent.
If the three angles in a triangle are congruent to the three angles in another triangle, then the two triangles are congruent.
If the three sides in a triangle are congruent to the three sides in another triangle, then the two triangles are congruent.
- 22. Multiple Choice
Select the statement that must be true.
Parallelograms have at least one right angle.
If a quadrilateral has opposite sides that are both congruent and parallel, then it is a parallelogram.
Parallelograms have congruent diagonals.
The height of a parallelogram is greater than the lengths of the sides.
- 23. Multiple Choice
EFGH is a parallelogram and angle HEF is a right angle.
Select all statements that must be true.
EFGH is a rectangle
Triangle HEF is congruent to triangle GFH
Triangle HEF is congruent to triangle FGH
ED is congruent to HD, DG, and DG
Triangle EDH is congruent to triangle HDG
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