Unit 2 Geometry

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 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

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.

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.

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

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

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.

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

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.