Unit2 Practice Problems

1. When rectangle ABCD is reflected across line EF , the image is DCBA . How do you know that segment AB  is congruent to segment DC ?

• 1. A rectangle has 2 pairs of parallel sides.

• Any 2 sides of a rectangle are congruent.

• 1. Congruent parts of congruent figures are corresponding.

• 1. Corresponding parts of congruent figures are congruent.

• EFGH is a rectangle

• EFGH has four congruent sides

• Diagonal FH bisects angles EFG and EHG

• Diagonal FH is perpendicular to side FE

• Angle FEH is congruent to angle FGH .

1. Triangle ABC is congruent to triangle DEF .  Select all the statements that are a result of corresponding parts of congruent triangles being congruent.

• 1. 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 FED 

1. Triangle HEF is the image of triangle FGH after a 180-degree rotation about point K . 

Select all statements that must be true

• Triangle

  FGH  is congruent to triangle FEH .

• Triangle EFH  is congruent to triangle GFH.

• Angle KHE  is congruent to angle KFG .

• 1. Angle GHK  is congruent to angle KHE.

• Segment GH  is congruent to segment EF .

1. When triangle ABC  is reflected across line AB , the image is triangle ABD . Why are segment AD and segment AC congruent?

• 1. Congruent parts of congruent figures are corresponding.

• 1. Corresponding parts of congruent figures are congruent.

• An isosceles triangle has a pair of congruent sides.

• 1. Segment AB  is a perpendicular bisector of segment DC .

1. Triangle ABC is congruent to triangle EDF . So, Kiran knows that there is a sequence of rigid motions that takes ABC to EDF .

2.  

Select all true statements after the transformations

• Angle A coincides with angle F .

• 1. Angle B coincides with angle D .

• Segment AC coincides with segment EF .

• 1. Segment BC coincides with segment ED .

• 1. Segment AB coincides with segment ED.

The triangles are congruent. Which sequence of rigid motions will take triangle XYZ onto triangle BCA ?

• 1. 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. 

• 1. 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. 

• 1. 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. 

• 1. 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 AC. 

Match each statement using only the information shown in the pairs of congruent triangles.

• Angle-Side-Angle

• 
• Side-Angle-Side

• 
• Side-Side-Side

• 

Triangle HEF is the image of triangle HGF after a reflection across line FH . Select all statements that must be true.

• 1. Triangle FGH is congruent to triangle FEH .

• 1. Triangle EFH is congruent to triangle GFH .

• 1. Triangle HFE is congruent to triangle FHG .

• 1. Segment EH  is congruent to segment FG.

• 1. Segment GH  is congruent to segment EH.

5. Quadrilateral ABCD is congruent to quadrilateral EFGH . So, Mai knows that there is a sequence of rigid motions that takes ABCD to EFGH .  

Select all true statements after the transformations.

• Angle A coincides with angle E.

• Angle B coincides with angle H.

• Segment AB coincides with segment EH .

• Segment BC coincides with segment FG .

• Segment CD coincides with segment EF .