ScienceMathGeometryCongruenceGeometry example #53304
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Geometry

Luka Rivera avatar Luka Rivera
8 September 2022
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14 test answers

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question
Triangle RST is rotated 180Β° about the origin, and then translated up 3 units. Which congruency statement describes the figures?
answer
?RST ? ?BAC
question
Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto's proof that was not included in Nessa's proof? Given: AngleB ? AngleN; BC ? NM; AngleC is right; AngleM is right Prove: TriangleABC ? TriangleQNM
answer
Angle
question
Could ?ABC be congruent to ?ADC by SSS? Explain.
answer
Yes, but only if BC ? DC.
question
Which rigid transformation would map TriangleABC to TriangleEDC?
answer
a rotation about point C
question
Triangle DEF is congruent to TriangleD'EF' by the SSS theorem. Which single rigid transformation is required to map TriangleDEF onto TriangleD'EF'?
answer
rotation
question
To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?
answer
AngleFGH ? AngleKGJ because vertical angles are congruent.
question
Which best explains whether or not ?ABC ? ?LMN?
answer
The figures are congruent because a 270Β° rotation about the origin and then a reflection over the x-axis will map ?ABC onto ?LMN.
question
Which best explains whether or not triangles RST and ACB are congruent?
answer
The figures are congruent. ?RST can be mapped to ?ACB by a reflection over the x-axis and a translation 2 units to the left.
question
What are the rigid transformations that will map ?ABC to ?DEF?
answer
Translate vertex A to vertex D, and then rotate ?ABC around point A to align the sides and angles.
question
How can ?ABC be mapped to ?XYZ? Triangles A B C and X Y Z are shown. The lengths of sides A B and X Y are 25 centimeters. The lengths of sides A C and X Z are 29 centimeters. Angles B A C and Y X Z are 36 degrees. Triangle A B C is slightly higher and to the left of triangle X Y Z. Triangle A B C is rotated to form triangle X Y Z. First, translate ____________________. Next, rotate ?ABC about B to align the sides and angles.
answer
vertex B to vertex Y
question
Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters. Is ?WXZ ? ?YZX? Why or why not?
answer
Yes, they are congruent by SAS.
question
Triangle ABC is rotated 45Β° about point X, resulting in triangle EFD. Triangle A B C is rotated 45 degrees about point X to form triangle E F D. The lengths of sides A C and D E are congruent, the lengths of sides A B and E F are congruent, and the lengths of sides D F and C B are congruent. If EF = 4.2 cm, DF = 3.6 cm, and DE = 4.5 cm, what is CB?
answer
3.6 cm
question
Which congruence theorem can be used to prove ?BDA ? ?DBC? Triangles B D A and D B C share side D B. Angles C B D and A D B are right angles. Sides C D and B A are congruent.
answer
HL
question
Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F. Which rigid transformation would map ?ABC to ?ABF?
answer
a reflection across the line containing BA