Question

Would appreciate the help

Answer 1

QUESTION 5

The opposite sides of a parallelogram are congruent.

$\Rightarrow 4x=20$

Divide  through by 4.

$\Rightarrow x=5$

Or

$5x=3x+10$

$5x-3x=10$

$2x=10$

$x=5$

QUESTION 6

The diagonals of a parallelogram bisect each other.

$\Rightarrow 4x=8$

Divide both sides by 4;

$\Rightarrow x=2$

Or

$5x=3x+4$

$5x-3x=4$

$2x=4$

$x=2$

QUESTION 7

The alternate interior angles of a parallelogram are equal.

$\Rightarrow 4x-20=2x$

Group similar terms;

$\Rightarrow 4x-2x=20$

Simplify and solve for x.

$\Rightarrow 2x=20$

$\Rightarrow x=10$

QUESTION 8

The opposite angles of a parallelogram are congruent.

$\Rightarrow 3x=2x+19$

Group similar terms;

$\Rightarrow 3x-2x=19$

Simplify;

$x=19$

QUESTION 9

The height, $h$ of this triangle can be determined using the absolute value method.

$h=|4-0|=4$ units.

The base,$b$ can be determined using the absolute value method.

$b=|7-0|=7$ units.

The hypotenuse, $d$ can be determined using the Pythagoras Theorem of distance formula;

$d=\sqrt{7^2+4^2}$

$d=\sqrt{49+16}$

$d=\sqrt{65}$ units.

The three sides are unequal. This is a scalene triangle.

QUESTION 10

The base of the triangle is

$b=|2--2|=4$ units.

The altitude of this triangle bisects the base. This means the triangle is isosceles.

We can use the distance formula to confirm this.

The to hypotenuse is

$T=\sqrt{(6-0)^2+(0-2)^2}$

$T=\sqrt{36+4}$

$T=\sqrt{40}$

$T=2\sqrt{10}$ units

The down hypotenuse is

$T=\sqrt{(6-0)^2+(0-2)^2}$

$D=\sqrt{36+4}$

$D=\sqrt{40}$

$D=2\sqrt{10}$ units

QUESTION 11

This parallelogram has all sides congruent, 8 units each.

It is called a square.

A square fits the definition of a rhombus. All sides are equal.

This is a rhombus.

QUESTION 12

One side of the parallelogram is $|3--1|=4$ units.

This is equal to the opposite side.

Another side is $\sqrt{(3-2)^2+(2--1)^2}=\sqrt{10}$ units.

This is also equal to the opposites side.

All the sides of this parallelogram are not congruent.

The diagonals do not also meet at right angles.

The parallelogram is not a rhombus.