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 $$ED$$ .

Angle $$A$$ coincides with angle $$F$$ .

Segment $$BC$$ coincides with segment $$ED$$ .

The triangles are congruent. Which sequence of rigid motions will take triangle $$XYZ$$ onto triangle $$BCA$$ ?

Translate $$XYZ$$ using directed line segment $$YC$$ . Rotate $$X$$ using $$C$$ as the center so that $$X$$ coincides with $$B$$ . Reflect $$X$$ across line $$CB$$ .

Translate $$XYZ$$ using directed line segment $$YC$$ . Rotate $$X$$ using $$C$$ as the center so that $$X$$ coincides with $$B$$ . Reflect $$X$$ across line $$AC$$ .

Translate $$XYZ$$ using directed line segment $$YC$$ . Rotate $$X$$ using $$C$$ as the center so that $$X$$ coincides with $$A$$ . Reflect $$X$$ across line $$CB$$ .

Translate $$XYZ$$ using directed line segment $$YC$$ . Rotate $$X$$ using $$C$$ as the center so that $$X$$ coincides with $$A$$ . Reflect $$X$$ 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 $$FEH$$ .

Segment $$FH$$ is congruent to segment $$HF$$ .

Angle $$GHK$$ is congruent to angle $$EFK$$ .

Segment $$HG$$ is congruent to segment $$FE$$ .

Triangle $$GFH$$ is congruent to triangle $$EFH$$ .

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 $$BAC$$ is congruent to angle $$EDF$$ .

Angle $$CBA$$ is congruent to angle $$FED$$ .

Segment $$AC$$ is congruent to segment $$EF$$ .

Angle $$BCA$$ is congruent to angle $$EDF$$ .

When triangle $$ABC$$ is reflected across line $$AB$$ , the image is triangle $$ABD$$ . Why is angle $$ACD$$ congruent to angle $$ADB$$ ?

Segment $$AB$$ is a perpendicular bisector of segment $$DC$$ .

Geometry | Unit 2 | Lesson 3: Congruent Triangles, Part 1 | Practice Problems

Authored by Illustrative Mathematics

Mathematics

6th Grade

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Geometry | Unit 2 | Lesson 3: Congruent Triangles, Part 1 | Practice Problems

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Corresponding parts of congruent figures are congruent.

Congruent parts of congruent figures are corresponding.

An isosceles triangle has a pair of congruent angles.

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