Illustrative Mathematics Geometry

When rectangle ABCD is reflected across line EF, the image is DCBA. How do you know that segment AB is congruent to segment DC?

• A rectangle has 2 pairs of parallel sides.

• Any 2 sides of a rectangle are congruent.

• Congruent parts of congruent figures are corresponding.

• Corresponding parts of congruent figures are congruent.

Select all statements that are true about the triangles.

• Triangles ABC and DCB are congruent by the Angle-Angle Triangle Congruence Theorem.

• Triangles ABC and BCD are congruent by the Angle-Side-Angle Triangle Congruence Theorem

• Triangles ABC and BCD are congruent by the Side-Side-Side Triangle Congruence Theorem.

• Triangles ABC and DCB are congruent by the Side-Angle-Side Triangle Congruence Theorem.

• Triangles ABC and DCB are congruent by the Side-Side-Side Triangle Congruence Theorem.

Which sequence of rigid motions will definitely work to take triangle GHJ onto triangle STU?

• Rotate GHJ using center G until GH is lined up with ST and then reflect over a line halfway between G'H'J' and STU.

• Translate GHJ by the directed line segment GS. Rotate G'H'J' using S as the center by angle H'ST. Reflect G''H''J'' over ST.

• Translate GHJ by the directed line segment GT. Rotate G'H'J' using T as the center by angle H'TS. Reflect G''H''J'' over ST.

• Translate GHJ by the directed line segment GS.Translate G'H'J' by the directed line segment H'T. Translate G''H''J'' by the directed line segment J''T.

Reflect triangle STU across line ST. Which of these is a valid reason why the image of U will coincide with J?

• The image of U and J are on the same side of ST and make the same angle with it at T.

• The image of U and J are the same distance along the same ray from T.

• The image of U and J will not coincide after reflection over ST.

• Line ST is the perpendicular bisector of the segment connecting U and J, because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment.

Here is parallelogram ABCD. Prove segment AM is congruent to segment CM.

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In parallelogram HIJK, the measure of angle H is 45 degrees. Find the measure of angle J. Explain how you know.

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In parallelogram HIJK, the measure of angle H is 45 degrees. Find the measure of angle K. Explain how you know.

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The measure of angle Q is 70 degrees. Find the measure of angle P.

Use rigid motions to prove that figure ABC is congruent to figure EFG.

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Triangle ABC is congruent to triangle EDF. So, Kiran knows that there is a sequence of rigid motions that takes ABC to EDF.

• Angle B coincides with angle D.

• Angle A coincides with angle F.

• Segment AC coincides with segment EF.

• Segment BC coincides with segment ED.

• Segment AB coincides with segment ED.