Quadrilaterals are squares

1 answer:

fomenos3 years ago

3 0

Basic answer
When is a quadrilateral a square?
When it has four right angles and four congruent sides.

Geometry Answer (just in case, since the question is vague)
How can you prove if a quadrilateral is a square?

It is a square if it is both a rectangle and a rhombus.

It is a rectangle if
a) It has a right angle and is a parallelogram
b) It has congruent diagonals and is a parallelogram
c) It has four right angles

It is a rhombus if
a) It has two adjacent sides congruent and is a parallelogram
b) Its diagonal bisects opposite angles and it is a parallelogram
c) Its diagonals perpendicular bisect each other

It is a parallelogram if
a) Two pairs of opposite sides parallel
b) Two pairs of opposite sides congruent
c) One pair of sides both congruent and parallel
d) The diagonals bisect each other
e) Two pairs of opposite angles congruent

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Question 14 of 25What is the complete factorization of the polynomial below?x³+x² + 4x+4O A. (x-1)(x+2)(x+2)B. (x + 1)(x + 2)(x

mote1985 [20]

GIVEN:

We are given the following polynomial;

$x^3+x^2+4x+4$

Required;

We are required to factorize this polynomial completely.

Step-by-step explanation;

To factorize this polynomial, we start by grouping;

$(x^3+x^2)+(4x+4)$

We now take the common factor in each group;

$\begin{gathered} x^2(x+1)+4(x+1) \\ \\ (x^2+4)(x+1) \end{gathered}$

Next, we factorize the first parenthesis. To do this we set the equation equal to zero and solve for x as follows;

$\begin{gathered} x^2+4=0 \\ \\ Subtract\text{ }4\text{ }from\text{ }both\text{ }sides: \\ \\ x^2=-4 \\ \\ Take\text{ }the\text{ }square\text{ }root\text{ }of\text{ }both\text{ }sides: \\ \\ x=\pm\sqrt{-4} \\ \\ x=(\pm\sqrt{-1}\times\sqrt{4}) \\ \\ x=\pm2i \end{gathered}$

Therefore, the factors of the other parenthesis are;