Given triangle ABC, if angle A = 40, a = 65, and angle B = 25. what is the length of b?
1 answer:
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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