Illustrative Mathematics - Geometry - Mathematics - Unit 2 - Lesson 3 - Formative Library | Library

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 B coincides with angle D.

Segment AC coincides with segment EF.

Segment AB coincides with segment ED.

Segment BC coincides with segment ED.

Angle A coincides with angle F.

G.CO.7

8.G.1.a

8.G.1.b

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 ray CA lines up with ray CE.
Explain why the image of C coincides with E.
Is triangle CBA congruent to triangle CDE? Explain your reasoning.

G.CO.7

8.G.1.a

8.G.1.b

G.CO.8

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 A. 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  coincides with X'. 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 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 B. Reflect X''Y''Z'' across line AC.

G.CO.7

8.G.1.a

8.G.1.b

G.CO.8

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

Triangle GFH is congruent to triangle EFH.

Segment EH is congruent to segment GH.

Triangle HGF is congruent to triangle FEH.

Segment HG is congruent to segment FE.

Segment FH is congruent to segment HF.

Angle GHK is congruent to angle EFK.

Angle KHE is congruent to angle KHG.

G.CO.7

8.G.1.a

8.G.1.b

G.CO.8

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?
Write a correct congruence statement for the pentagons.

G.CO.7

8.G.1.a

8.G.1.b

G.CO.8

Triangle ABC is congruent to triangle DEF.  Select all the statements that are a result of corresponding parts of congruent triangles being congruent.

Segment BC is congruent to segment EF.

Angle BCA is congruent to angle EDF.

Segment AC is congruent to segment EF.

Angle CBA is congruent to angle DEF.

Angle BAC is congruent to angle EDF.

G.CO.7

8.G.1.a

8.G.1.b

G.CO.8

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.

An isosceles triangle has a pair of congruent angles.

Congruent parts of congruent figures are corresponding.

Segment AB is a perpendicular bisector of segment DC.

G.CO.7

8.G.1.a

8.G.1.b

G.CO.8

Line DE is parallel to line BC.

What is the measure of angle EAC?
What is the measure of angle DAB?

G.CO.7

8.G.1.a

8.G.1.b

G.CO.8

This lesson is from Illustrative Mathematics. Geometry, Unit 2, Lesson 3. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/2/3/index.html ; accessed 29/July/2021.

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