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creativ13 [48]
3 years ago
7

Bastian was able to map quadrilateral OPQROPQRO, P, Q, R onto ONMLONMLO, N, M, L using a reflection and a dilation.

Mathematics
1 answer:
zaharov [31]3 years ago
5 0

Answer:

C. There is no error. This is a correct conclusion.

Step-by-step explanation:

Reflection is a transformation in which a given image is flipped across a reflection line  to create the image. Each point of the image (e.g ONML) maintained their distance from the line as the initial object (e.g OPQR). The size of the object and image are the same after a reflection.

Dilation involve resizing the dimensions of a given object to produce an image of the same shape. It requires a scale factor to either increase or decrease the dimensions of the object.

Comparing quadrilaterals OPQR and ONML. Drawing a reflection line vertically through O, it can be observed that OPQR was first reflected. Then  enlarged by a scale factor to produce ONML, thus dilation.

Therefore, there is no error in Bastian's conclusion.

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Step-by-step explanation:

1. AB is parallel to CD.                                1. Given

  BC is parallel to DE.

  m<BAC=64 and m<CBA =56

2. m<BAC + m<CBA + m<BCA =180       2. The angles in a triangle add up to       180

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4. 120 + m<BCA=180 4. Addition property of equality.

5. m<BCA=60 5. Subtraction property of equality.

6. BC is a transversal that cuts through parallel lines AB and CD.

6. Def. of transversal.

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11. M<DCE =64 11. Subtraction property of equality.

12. DC is a transversal that cuts through parallel line BC and DE.

12. Def of transversal.

13. m<EDC= m<BCD 13. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

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15. m<EDC+m<DCE+m<Dec=180. 15. Angle addition postulate

16. 56+64+m<dec = 180.16 Substitution property of equality.

17. 120+ m<dec = 180. Addition property of equality.

18. m<dec = 60 18. Subtraction property of equality.

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