Ms.Alvarez's math class surveyed 10 students in 6th grade and 10 students in 7th grade. The class asked how many hours of chores
each student did the previous weekend. The results were displayed in two histograms.
2 answers:
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Answer:
A rhombus is a parallelogram with four congruent sides.
So, all sides of rhombus ABCD are congruent.
i.e,
Also, we know that the diagonals of a parallelogram bisect each other.
Since a rhombus is a parallelogram.
By property of rhombus , if point N is the intersection of the diagonals as shown in the figure, then
.....[1]
In ΔJNM and ΔJNK
[side] [by (1)]
[side] [Given]
By reflexive property states that a segment is congruent to itself:
[Side] [Reflexive Property]
SSS(Side-Side-Side) postulates states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
then by SSS congruence,
By CPCT [Corresponding Part of congruent triangles are congruent]
Since, JNM and JNK are corresponding angles therefore,
Linear pair theorem states that two angles that form a linear pair are supplementary.
By linear pair theorem, JNM and JNK are supplementary
this mean:
Since, the angles are congruent i.e,
so;
or
2
Simplify:
also;
therefore, the diagonals of JKLM are perpendicular to each other i,e