Answer:
Part 10)
a) [tex]OM=46\ units[/tex]
b) [tex]PN=23\ units[/tex]
c) [tex]ON=23\sqrt{2}\ units[/tex]
d) [tex]MN=23\sqrt{2}\ units[/tex]
Part 12) x=11
Part 14) see the explanation
Step-by-step explanation:
Part 10) we know that
In a square all four sides are congruent
The diagonals of a square are congruent and bisect each other at right angles
Part a)
Find the length of diagonal OM
we know that
[tex]OM=LN[/tex] ---> the diagonals are congruent
we have
[tex]LN=46\ units[/tex]
therefore
[tex]OM=46\ units[/tex]
Part b)
Find the length of PN
we know that
[tex]PN=PL[/tex] ---> remember that the diagonals bisect each other
[tex]PN=\frac{LN}{2}[/tex]
we have
[tex]LN=46\ units[/tex]
substitute
[tex]PN=\frac{46}{2}=23\ units[/tex]
Part c)
Find the length of ON
Applying the Pythagorean Theorem
[tex]OM^2=ON^2+MN^2[/tex]
we know that
[tex]ON=MN[/tex] ----> remember that all four sides are congruent
so
[tex]OM^2=2ON^2[/tex]
[tex]OM=46\ units[/tex]
substitute
[tex]46^2=2ON^2[/tex]
[tex]2,116=2ON^2[/tex]
[tex]1,058=ON^2[/tex]
[tex]ON=\sqrt{1,058}\ units[/tex]
simplify
[tex]ON=23\sqrt{2}\ units[/tex]
Part d)
Find the length of MN
we know that
[tex]MN=ON[/tex] ----> remember that all four sides are congruent
we have
[tex]ON=23\sqrt{2}\ units[/tex]
therefore
[tex]MN=23\sqrt{2}\ units[/tex]
Part 12) we know that
The diagonals of a square bisect its angles
Remember that the interior angles of a square is 90 degrees
so
[tex](6x-21)\°=45\°[/tex]
solve for x
[tex]6x=45+21\\6x=66\\x=11[/tex]
Part 14) we know that
A parallelogram has opposite parallel sides, so a parallelogram will always have consecutive supplementary angles.
The rectangle, rhombus and a square are all parallelograms
therefore
parallelograms, rectangles,rhombi and squares will always have consecutive supplementary angles.
