Module1_EOM

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.

• 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.

• 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.

• create an equilateral triangle

• 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.

• a line perpendicular to a given line

• 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.

Tags

G.CO.12

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

Find the values for x and y.

Tags

G.CO.9

G.CO.10

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

Given: AB ∥ ED and AD and BE bisect each other

Part A

Complete the proof that △ABC≅△DEC. Select from the drop-down lists to justify the steps in the proof.

AB ∥ ED Given

AD and BE bisect each other Given

m∠ABC = m∠DEC ​ (a)   ​ ​ ​

m∠ACB = m∠DCE ​ (b)  

EC = BC ​ (c)  

△ABC ≅ △DEC​ is ​ (d)   congruence

• Alternate interior angles are equal in measure
• Vertical angles are equal in measure
• Corresponding angles are equal in measure
• Definition of a segment bisector
• Definition of an angle bisector
• Definition of a midpoint
• ASA
• AAS
• SAS
• SSS

Tags

G.CO.7

G.CO.8

Part B

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

In △ABC, M is the centroid and AD, BE, and CF are all medians. (Figure is not drawn to scale.)

If EM=11, AM=16, and CF=27, what are the lengths of BE, DM, CM? (in that order)

Tags

G.CO.10

Which triangle pairs are not necessarily congruent?  Select all that apply.

• 
• 
• 
• 
• 

Tags

G.CO.8

In the figure, AB is a midsegment of ​△XYZ​, CD is a midsegment of △XAB, and AY ≅ BZ.

Which statements are true?  Select all that apply.

​
​ (a)   ​ (b)   ​ ​ (c)  

• ∠Y ≅ ∠Z
• ∠X ≅ ∠Y
• XC ≅ XD
• XZ ≅ YZ
• △XYZ is isosceles
• △XYZ is equilateral

Tags

G.CO.10