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This printable supports Common Core Mathematics Standards HSG-CO.B.7

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# Triangle Congruence Through Rigid Motions (Grade 10)

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## Triangle Congruence Through Rigid Motions

1.
If triangle ABC is congruent to triangle EDF, there must always exist some rigid transformations - reflections, rotations, and/or translations - that can map triangle ABC onto triangle EDF.
1. True
2. False
2.
You are given two triangles, ABC and FGH. There is a sequence of translations and reflections that map triangle ABC to triangle FGH, such that $bar{AB}$ maps to $bar{GH}$ and $bar{AC}$ maps to $bar{GF}$. Which of the following statements is correct?
1. There is not enough information to say if the triangles are congruent.
2. $Delta ABC ~= Delta HGF$
3. $Delta ABC ~= FHG$
4. $Delta ABC ~= Delta GHF$
3.
Triangle ABC undergoes the following transformations: a vertical translation of +5 units, a reflection about the x-axis, and a dilation by factor 2. The resulting triangle is labeled LMN. For the two triangles, we have $ang M ~= ang A$ and $angN ~= ang B$. Which of the following is true?
1. These triangles are not congruent.
2. $Delta ABC ~= Delta MNL$
3. $Delta ABC ~= Delta NML$
4. $Delta ABC ~= Delta LNM$
4.
If one triangle can be mapped onto another triangle through a sequence of rigid transformations, which of the following MUST be true? Choose all that apply.
1. The name of the triangles is the same.
2. The corresponding sides of the triangles are congruent.
3. The corresponding angles of the triangles are congruent.
4. The orientation of the triangles is the same.
5.
Triangle ABC, whose vertices are $(-5,1), (-3,4),$ and $(-2,1)$, is reflected over the y-axis and then rotated 90° clockwise about the origin. The points, in no particular order, resulting from the transformation are $(1,-2), (1,-5),$ and $(4,-3)$. Labeling these points as F, G, and H respectively, which of the following is true?
1. No relation between triangle ABC and transformed points.
2. $Delta ABC ~= Delta FHG$
3. $Delta ABC ~= Delta HGF$
4. $Delta ABC ~= Delta GHF$
6.
Which of the following transformations would show if $Delta ABC ~= Delta ADC ?$ 1. Translate triangle ABC down by vertical distance between $bar{AC}$ and point B.
2. Reflect triangle ABC over the line containing $bar{AC}$.
3. Rotate triangle ABC 180° around midpoint of $bar{AC}$.
4. Translate triangle ABC down by half the vertical length between $bar{AC}$ and point B, and then rotate it 180° about its centroid.
7.
Which of the following transformations would show if $Delta ABD ~= Delta CDB ?$ 1. Translate triangle ABD right by length of $bar{AD}$.
2. Reflect triangle ABD over the line containing $bar{BD}$.
3. Rotate triangle ABD 180° about the midpoint of $bar{BD}$.
4. Reflect triangle ABD over the line containing $bar{BD}$ then translate $1/4 vec{BD}$.
8.
Which of the following transformations would show if $Delta ABF ~= Delta ECD ?$ 1. Translate triangle ABF right by the length of $bar{FD}$.
2. Reflect triangle ABF about the line joining the midpoints of $bar{BC}$ and $bar{FD}$.
3. Rotate triangle ABF 180° about the midpoint of the line joining the midpoints of $bar{BC}$ and $bar{FD}$.
4. Translate triangle ABF right by the length of $bar{FE}$.
9.
In the regular hexagon pictured, the center is M (not pictured). Which of the following transformations show that $Delta BMC ~= Delta DME ?$ Choose all correct answers. 1. Reflect triangle BMC over the line joining the midpoints of $bar{CD}$ and $bar{AF}$.
2. Rotate triangle BMC 120° counterclockwise about point M.
3. Translate triangle BMC right the length of $bar{CD}$, then rotate it 120° clockwise about its centroid.
4. Rotate triangle BMC 60° clockwise about point M, then reflect it over the line passing through C and F.
10.
In the diagram below, Shannon knows that $ang BAC ~= ang BCA ~= ang DFE ~= ang DEF$ and that $bar{BE}$ || $bar{AD}$. To prove that the two triangles, ABC and FDE, are congruent, she proposes the following sequence of transformations to map $Delta ABC$ onto $Delta FDE$: translate triangle ABC up by the length of the vertical distance between line segments $bar{BE}$ and $bar{AD}$, then translate triangle ABC right by the length of $bar{BF}$ plus half the length of $bar{FE}$, then reflect it over the line containing points B and E. Is this correct and why? 1. No, the sequence of transformations is incorrect.
2. No, you have to use a triangle congruence theorem.
3. Yes, if the triangles map exactly onto each other (corresponding sides and angles are congruent), this proves $Delta ABC ~= Delta FDE$.
4. It is unnecessary, since we can determine that $ang ABC ~= ang FDE$, and so already know the triangles are congruent.        You need to be a HelpTeaching.com member to access free printables.