Question

Someone help me solve 10-16 please thank you!

Answer 1

Part 10)

a)
`OM=46\ units`

b)
`PN=23\ units`

c)
`ON=23√(2)\ units`

d)
`MN=23√(2)\ units`

Part 12) x=11

Part 14) see the explanation

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

`OM=LN` ---> the diagonals are congruent

we have

`LN=46\ units`

therefore

`OM=46\ units`

Part b)

Find the length of PN

we know that

`PN=PL` ---> remember that the diagonals bisect each other

`PN=(LN)/(2)`

we have

`LN=46\ units`

substitute

`PN=(46)/(2)=23\ units`

Part c)

Find the length of ON

Applying the Pythagorean Theorem

`OM^2=ON^2+MN^2`

we know that

`ON=MN` ----> remember that all four sides are congruent

so

`OM^2=2ON^2`

`OM=46\ units`

substitute

`46^2=2ON^2`

`2,116=2ON^2`

`1,058=ON^2`

`ON=√(1,058)\ units`

simplify

`ON=23√(2)\ units`

Part d)

Find the length of MN

we know that

`MN=ON` ----> remember that all four sides are congruent

we have

`ON=23√(2)\ units`

therefore

`MN=23√(2)\ units`

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

`(6x-21)\°=45\°`

solve for x

`6x=45+21\\6x=66\\x=11`

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.