Congruences Parallel Line

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

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.

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.

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.

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.

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.

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.

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

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.

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.