Rigid Motions and the Constructions

Which rigid motion would map △ABC onto △DEC?

• 180°

  rotation about the center of △ABC

• reflection across a horizontal line through point C

• 180°

  rotation about point C

• reflection across a vertical line through point C

Tags

G.CO.7

G.CO.8

Consider the steps for four geometric constructions. Match each set of steps with the correct geometric construction. Drag each geometric construction to the box above the correct set of steps.

• create an equilateral triangle

• Draw AB.

  Draw a point not on AB

  and label the point C.

  Draw circle C

  so that it intersects AB

  at two distinct points.

  Label the points of intersection as D

  and E.

  Draw circle D

  with radius DE.

  Draw circle E

  with radius ED.

  Label either intersection point of circles D

  and E as F.

  Draw CF.

• construct a perpendicular bisector

• Draw an angle and label the vertex B.

  Draw EG.

  Draw a circle with center at B.

  Label the intersections of circle B with the sides of the angle as A

  and C.

  Draw a circle with center at E

  and a radius BA.

  Label the intersection of circle E with EG as F.

  Draw a circle with center at F and a radius CA.

  Label either intersection of circle E and circle F as D.

  Draw ED.

• a line perpendicular to a given line

• Draw AB.

  Draw a circle with center at A

  and a radius AB.

  Draw a circle with center at B

  and a radius BA.

  Label the points of intersections of circles A and B as C and D.

  Draw CD.

• copy an angle

• Draw AB.

  Draw a circle with center at A

  and a radius AB.

  Draw a circle with center at B

  and a radius BA.

  Label one point of intersection of circles A and B as C.

  Draw AC and BC.

Tags

G.CO.12

Which rigid motion or sequence of rigid motions maps parallelogram ABCD onto parallelogram JKLM? Select all that apply.

• Reflection across l₁

• 
  Rotation of 180° about point P

• Rotation of 180° about point P followed by a reflection across l₂

• Reflection across l₁ followed by a 90° rotation about point P

• Reflection across l₁ followed by a second reflection across l₂
  

Tags

G.CO.3

In pentagons ABCDE and VWXYZ, AE ≅ AB ≅ VZ ≅ VW and ED ≅ DC ≅ BC ≅ ZY ≅ YX ≅ WX. Are pentagons ABCDE and VWXYZ congruent and why?

• Yes, because rigid motions map segments onto segments of equal length, and each side of ABCDE can be mapped onto a corresponding side of VWXYZ.

• Yes, because rigid motions map angles onto angles of equal measure, and each angle of ABCDE

  can be mapped onto a corresponding angle of VWXYZ.

• • No, because rigid motions map segments onto segments of equal length, and both ABCDE and VWXYZ have segments of two different lengths.

• No, because rigid motions map angles onto angles of equal measure, and ABCDE has right angles while VWXYZ has no right angles.

Tags

G.CO.6

Does the transformation appear to be a rigid motion?

• Yes, distances are preserved.

• Yes, angle measures are preserved.

• Yes, both distances and angle measures are preserved.

• No, distances are not preserved.

• A

• B

• C

• D

What rigid motion from the pre-image to the prime image?

• transformation

• rotation

• translation

• reflection

CF is perpendicular to AB, and CF bisects AB. Points D and E are points on CF. Which pairs of segments must be congruent? Select all that apply.

• AE ≅BE

• AB ≅ CF

• CE ≅ EF

• AD ≅ BD

• AE ≅AF

Tags

G.CO.12

Identify the transformation:

• Rotation

• Reflection

• Translation

• Dilation

Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D