Congruent Parts, Part 1

ID: kimum-fuboz
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Congruent Parts, Part 1

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Problem 1

1) When rectangle ABCDABCD is reflected across line EFEF, the image is DCBADCBA. How do you know that segment ABAB is congruent to segment DCDC?

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a) A rectangle has 2 pairs of parallel sides.\text{A rectangle has 2 pairs of parallel sides.}b) Any 2 sides of a rectangle are congruent.\text{Any 2 sides of a rectangle are congruent.}c) Congruent parts of congruent figures are corresponding.\text{Congruent parts of congruent figures are corresponding.}d) Corresponding parts of congruent figures are congruent.\text{Corresponding parts of congruent figures are congruent.}
Problem 2

2) 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 b) EFGHEFGH has 4 congruent sides. \quad\quad c) Diagonal FHFH bisects angles EFGEFG and EHGEHG.

d) Diagonal FHFH is perpendicular to side FEFE. \quad\quad e) Angle FEHFEH is congruent to angle FGHFGH.

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Problem 3


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3) Reflect right triangle ABCABC across line BCBC.

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4) Classify triangle ACAACA' according to its side lengths.

5) Explain how you know.

Problem 4

6) Triangles FADFAD and DCEDCE are translations of triangle ABCABC.

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

a) Points BB, AA, and FF are collinear. \quad\quad b) The measure of angle BCABCA is the same as the measure of angle CEDCED.

c) Line ADAD is parallel to line BCBC. \quad\quad d) The measure of angle CEDCED is the same as the measure of angle FADFAD.

e) The measure of angle DACDAC is the same as the measure of angle BCABCA.

f) Triangle ADCADC is a reflection of triangle FADFAD.

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Problem 5

Triangle ABCABC is congruent to triangles BADBAD and CEACEA.

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7) Explain why points DD, AA, and EE are collinear.

8) Explain why line DEDE is parallel to line BCBC.

Problem 6


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9) Identify a figure that is the result of a rigid transformation of quadrilateral ABCDABCD.

10) Describe a rigid transformation that would take ABCDABCD to that figure.