1. Line SD is a line of symmetry for figure AXPDZHMS. Noah says that AXPDS is congruent to HMZDS because sides AX and HM are corresponding.
Part a: Why is Noah's congruence statement incorrect?
Part b: Write a correct congruence statement for the pentagons.
Answers
Answer/Step-by-step explanation:
Part A:
If a figure is divided into two equal halves by a line of symmetry, each of the pair the corresponding parts will be congruent to the other part.
Thus, based on the Symmetric Figures Theorem, the two parts in the question above are congruent as a result of the line of symmetry, line SD, which makes one part the mirror image of the other.
Therefore, Noah's congruence statement is of the pentagons is incorrect.
Part B:
Based on Symmetric Figures Theorem, AXPDS is congruent to MHZDS as the line of symmetry, line SD, makes one a mirror image of the other.
The line of symmetry of the quadrilateral AXPDZHMS = The line SD
Therefore, given that SD is congruent to SD by reflexive property, we have;
AXPDS is congruent to MHZDS
Part a: The reason why Noah's congruency statement is incorrect is the
order of the lettering in the statement, and the part of the selected that do
not directly show congruency, which are;
Noah's statement; AXPDS is congruent to HMZDS because sides AX and HM are corresponding.Part b: The correct congruency statement is presented as follows;
AXPDS is congruent to MHZDS because SD and SD are reflexive and corresponding sides and are therefore congruent. Therefore, by the converse of the Congruent Parts of Congruent Figures are Congruent, CPCFC we have, AXPDS is congruent to MHZDSLearn more here:
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