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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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

Tags

CCSS.HSG.CO.B.7

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

Tags

CCSS.HSG.CO.B.6

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.

Tags

CCSS.HSG.CO.B.6

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.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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

Tags

CCSS.HSG.CO.C.9

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.

Tags

CCSS.HSG.CO.C.10