Question

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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=√(7^2+4^2)`

`d=√(49+16)`

`d=√(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=√((6-0)^2+(0-2)^2)`

`T=√(36+4)`

`T=√(40)`

`T=2√(10)` units

The down hypotenuse is

`T=√((6-0)^2+(0-2)^2)`

`D=√(36+4)`

`D=√(40)`

`D=2√(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
`√((3-2)^2+(2--1)^2)=√(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.