QUESTION 5
The opposite sides of a parallelogram are congruent.
[tex]\Rightarrow 4x=20[/tex]
Divide through by 4.
[tex]\Rightarrow x=5[/tex]
Or
[tex]5x=3x+10[/tex]
[tex]5x-3x=10[/tex]
[tex]2x=10[/tex]
[tex]x=5[/tex]
QUESTION 6
The diagonals of a parallelogram bisect each other.
[tex]\Rightarrow 4x=8[/tex]
Divide both sides by 4;
[tex]\Rightarrow x=2[/tex]
Or
[tex]5x=3x+4[/tex]
[tex]5x-3x=4[/tex]
[tex]2x=4[/tex]
[tex]x=2[/tex]
QUESTION 7
The alternate interior angles of a parallelogram are equal.
[tex]\Rightarrow 4x-20=2x[/tex]
Group similar terms;
[tex]\Rightarrow 4x-2x=20[/tex]
Simplify and solve for x.
[tex]\Rightarrow 2x=20[/tex]
[tex]\Rightarrow x=10[/tex]
QUESTION 8
The opposite angles of a parallelogram are congruent.
[tex]\Rightarrow 3x=2x+19[/tex]
Group similar terms;
[tex]\Rightarrow 3x-2x=19[/tex]
Simplify;
[tex]x=19[/tex]
QUESTION 9
The height, [tex]h[/tex] of this triangle can be determined using the absolute value method.
[tex]h=|4-0|=4[/tex] units.
The base,[tex]b[/tex] can be determined using the absolute value method.
[tex]b=|7-0|=7[/tex] units.
The hypotenuse, [tex]d[/tex] can be determined using the Pythagoras Theorem of distance formula;
[tex]d=\sqrt{7^2+4^2}[/tex]
[tex]d=\sqrt{49+16}[/tex]
[tex]d=\sqrt{65}[/tex] units.
The three sides are unequal. This is a scalene triangle.
QUESTION 10
The base of the triangle is
[tex]b=|2--2|=4[/tex] 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
[tex]T=\sqrt{(6-0)^2+(0-2)^2}[/tex]
[tex]T=\sqrt{36+4}[/tex]
[tex]T=\sqrt{40}[/tex]
[tex]T=2\sqrt{10}[/tex] units
The down hypotenuse is
[tex]T=\sqrt{(6-0)^2+(0-2)^2}[/tex]
[tex]D=\sqrt{36+4}[/tex]
[tex]D=\sqrt{40}[/tex]
[tex]D=2\sqrt{10}[/tex] 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 [tex]|3--1|=4[/tex] units.
This is equal to the opposite side.
Another side is [tex]\sqrt{(3-2)^2+(2--1)^2}=\sqrt{10}[/tex] 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.
