Illustrative Mathematics - Geometry - Mathematics - Unit 2 - Lesson 4

What is the least amount of information that you need to construct a triangle congruent to this one?

Tags

N.Q.3

G.CO.1

G.CO.8

Triangle ABC is congruent to triangle EDF. So, Mai knows that there is a sequence of rigid motions that takes ABC to EDF. Select all true statements after the transformations:

• {"blocks":[{"key":"0","text":"Angle A coincides with angle E.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":1,"style":"BOLD"},{"offset":29,"length":1,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"0","text":"Angle B coincides with angle F.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":1,"style":"BOLD"},{"offset":29,"length":1,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"0","text":"Segment AB coincides with segment EF.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":8,"length":2,"style":"BOLD"},{"offset":34,"length":2,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"0","text":"Segment BC coincides with segment DF.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":8,"length":2,"style":"BOLD"},{"offset":34,"length":2,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"cqebq","text":"Segment AC coincides with segment ED.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":8,"length":2,"style":"BOLD"},{"offset":34,"length":2,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}

Tags

N.Q.3

G.CO.1

G.CO.8

A rotation by angle ACE using point C as the center takes triangle CBA onto triangle CDE. Explain why the image of segment CB lines up with ray CD.Explain why the image of B coincides with D.Is triangle ABC congruent to triangle EDC? Explain your reasoning.

Tags

N.Q.3

G.CO.1

G.CO.8

Line EF is a line of symmetry for figure ABECDF. Clare says that ABEF is congruent to CDFE because sides AB and CD are corresponding. Why is Clare's congruence statement incorrect?Write a correct congruence statement for the pentagons.

Tags

N.Q.3

G.CO.1

G.CO.8

Triangle HEF is the image of triangle HGF after a reflection across line FH. Select all statements that must be true.

• {"blocks":[{"key":"0","text":"Triangle FGH is congruent to triangle FEH.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":9,"length":3,"style":"BOLD"},{"offset":38,"length":3,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"0","text":"Triangle EFH is congruent to triangle GFH.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":9,"length":3,"style":"BOLD"},{"offset":38,"length":3,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"0","text":"Angle HFE is congruent to angle FHG.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":3,"style":"BOLD"},{"offset":32,"length":3,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"0","text":"Angle EFG is congruent to angle EHG.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":6,"length":3,"style":"BOLD"},{"offset":32,"length":3,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}
• {"blocks":[{"key":"0","text":"Segment EH is congruent to segment FG.","type":"unstyled","depth":0,"inlineStyleRanges":[{"offset":8,"length":2,"style":"BOLD"},{"offset":35,"length":2,"style":"BOLD"}],"entityRanges":[],"data":{}}],"entityMap":{}}

Tags

N.Q.3

G.CO.1

G.CO.8

This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure onto itself.

Tags

N.Q.3

G.CO.1

G.CO.8