Congruent Triangles, Part 2

ID: hiboz-tiron
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Congruent Triangles, Part 2

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Problem 1

Match each statement using only the information shown in the images of pairs of congruent triangles. Write the number of the corresponding image in the answer box.

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1) In the 2 triangles there are 3 pairs of congruent sides.

2) The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.

3) The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

Problem 2

4) Sketch the unique triangles that can be made with angle measures 40°40\degree and 100°100\degree and side length 3.

5) How do you know you have sketched all possibilities?

Problem 3

6) What is the least amount of information that you need to construct a triangle congruent to this one?

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Problem 4

7) Triangle ABCABC is congruent to triangle EDFEDF. So, Mai knows that there is a sequence of rigid motions that takes ABCABC to EDFEDF.

Select all true statements after the transformations. Write each corresponding letter in the answer box and separate letters with commas.

a) Angle AA coincides with angle EE. \quad\quad b) Angle BB coincides with angle FF. \quad\quad c) Segment ABAB coincides with segment EFEF. \quad\quad d) Segment BCBC coincides with segment DFDF. \quad\quad e) Segment ACAC coincides with segment EDED.

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Problem 5

A rotation by angle ACEACE using point CC as the center takes triangle CBACBA onto triangle CDECDE.

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8) Explain why the image of segment CBCB lines up with ray CDCD.

9) Explain why the image of BB coincides with DD.

10) Is triangle ABCABC congruent to triangle EDCEDC?

True or false? Write below.

11) Explain your reasoning.

Problem 6

Line EFEF is a line of symmetry for figure ABECDFABECDF. Clare says that ABEFABEF is congruent to CDFECDFE because sides ABAB and CDCD are corresponding.

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12) Why is Clare's congruence statement incorrect?

13) Write a correct congruence statement for the quadrilaterals.

Problem 7

14) Triangle HEFHEF is the image of triangle HGFHGF after a reflection across line FHFH.

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 HFEHFE is congruent to angle FHGFHG. \quad\quad d) Angle EFGEFG is congruent to angle EHGEHG. \quad\quad e) Segment EHEH is congruent to segment FGFG. \quad\quad f) Segment GHGH is congruent to segment HEHE.

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Problem 8

15) When rectangle ABCDABCD is reflected across line EFEF, the image is BADCBADC. How do you know that segment ADAD is congruent to segment BCBC?

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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) Corresponding parts of congruent figures are congruent.\text{Corresponding parts of congruent figures are congruent.}d) Congruent parts of congruent figures are corresponding.\text{Congruent parts of congruent figures are corresponding.}
Problem 9

16) This design began from the construction of a regular hexagon. Describe a rigid motion that will take the figure onto itself.

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