Congruent Parts, Part 2

ID: jaraj-pofib
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Congruent Parts, Part 2

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Problem 1

Line SDSD is a line of symmetry for figure AXPDZHMSAXPDZHMS. Noah says that AXPDSAXPDS is congruent to HMZDSHMZDS because sides AXAX and HMHM are corresponding.

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1) Why is Noah’s congruence statement incorrect?

2) What pentagon is congruent to pentagon AXPDSAXPDS?

Problem 2

Figure MBJKGHMBJKGH is the image of figure AFEKJBAFEKJB after being rotated 90 degrees counterclockwise about point KK.

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3) Draw a segment in figure AFEKJBAFEKJB to create a quadrilateral.

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4) Draw the image of the segment when rotated 90 degrees counterclockwise about point KK.

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5) Write a congruence statement for the quadrilateral you created in figure AFEKJBAFEKJB and the image of the quadrilateral in figure MBJKGHMBJKGH.

Problem 3

6) Triangle HEFHEF is the image of triangle FGHFGH after a 180 degree rotation about point KK.

Select all statements that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) Triangle FGHFGH is congruent to triangle FEHFEH. \quad\quad b) Triangle EFHEFH is congruent to triangle GFHGFH. \quad\quad c) Angle KHEKHE is congruent to angle KFGKFG. \quad\quad d) Angle GHKGHK is congruent to angle KHEKHE. \quad\quad e) Segment EHEH is congruent to segment FGFG. \quad\quad f) Segment GHGH is congruent to segment EFEF.

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Problem 4

7) When triangle ABCABC is reflected across line ABAB, the image is triangle ABDABD. Why are segment ADAD and segment ACAC congruent?

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a) Congruent parts of congruent figures are corresponding.\text{Congruent parts of congruent figures are corresponding.}b) Corresponding parts of congruent figures are congruent.\text{Corresponding parts of congruent figures are congruent.}c) An isosceles triangle has a pair of congruent sides.\text{An isosceles triangle has a pair of congruent sides.}d) Segment AB is a perpendicular bisector of segment DC.\text{Segment } AB \text{ is a perpendicular bisector of segment } DC \text{.}
Problem 5

Elena needs to prove angles BEDBED and BCABCA are congruent. Provide reasons to support each of her statements.

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8) Line mm is parallel to line ll.

9) Angles BEDBED and BCABCA are congruent.

Problem 6

10) Triangle FGHFGH is the image of isosceles triangle FEHFEH after a reflection across line HFHF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent. Write each corresponding letter in the answer box and separate letters with commas.

a) EFGHEFGH is a rectangle. \quad\quad\quad b) EFGHEFGH is a rhombus. \quad\quad\quad c) Diagonal FHFH bisects angles EFGEFG and EHGEHG. \quad\quad\quadd) Diagonal FHFH is perpendicular to side FEFE. \quad\quad e) Angle EHFEHF is congruent to angle FGHFGH. \quad\quad f) Angle FEHFEH is congruent to angle FGHFGH.

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Problem 7

This design began from the construction of a regular hexagon.

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11) Draw 1 segment so the diagram has another hexagon that is congruent to hexagon ABCIHGABCIHG.

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12) Explain why the hexagons are congruent.