Unit 2 Geometry

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 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.

Triangle HEF is the image of triangle FGH after a 180 degree rotation around point K. Select all statements that must be true.

• Triangle HGF is congruent to triangle FEH.

• Angle GHK is congruent to angle EFK

• Segment HG is congruent to segment FE.

• Segment FH is congruent to segment HF.

• Angle KHE is congruent to angle KHG.

Line SD is a line of symmetry for figure ASMHZDPX. Tyler says that ASDPX is congruent to SMDZH because sides AS and MS are corresponding. Why is Tyler's congruence statement incorrect?

• Because SMD and ASD are NOT congruent. He needs to be more careful of the order in which he labels his figures.

• ASDPX and SMDZH are not congruent figures.

• Line SD is not a line of symmetry.

• Tyler's statement is correct.

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 FED.

When triangle ABC is reflected 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 a perpendicular bisector of segment DC.

• An isosceles triangle has a pair of congruent angles.

Line DE is parallel to line BC. What is the measure of angle EAC?

• a degrees

• b degrees

• c degrees

• a+b degrees

Explain why the image of ray CA lines up with ray CE.

• Because they are parallel

• Because they are perpendicular

• Because the rotation was defined this way.

• Because they intersect at a point

Explain why the image of A coincides with E.

• Because A and E are identical.

• Due to the transformation properties.

• Because E and A are the same distance from C.

• Because they are on the same plane.

Write a correct congruence statement for the pentagons.

• Pentagon ASDPX ≅ Pentagon MSDZH

• Pentagon ASDPX ≅ Pentagon SMHZD

• Pentagon HZDSM ≅ Pentagon MSDZH

• None of these.

Line DE is parallel to line BC. What is the measure of angle DAB?

• a degrees

• b degrees

• c degrees

• d degrees