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Mathematics

1 answer:

Naddika [18.5K]3 years ago

4 0

The terms $-12x^2y$ and $4x^2y$ can be added to $3x^2y$ to result in a monomial.

Step-by-step explanation:

Given term is;

$3x^2y$

A monomial is an algebraic expression that consists of only one term.

So in the given expressions, we will add the terms which have same variables as given terms.

Given options are;

$3xy\\-12x^2y\\2x^2y^2\\7xy^2\\-10x^2\\4x^2y\\3x^3$

The terms $-12x^2y$ and $4x^2y$ can be added to $3x^2y$ to result in a monomial.

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3 years ago

In the figure, and bisect each other. Complete the statements to prove that quadrilateral ABCD is a parallelogram.

Alisiya [41]

Observe the figure below.

Statement Reason

1. AC and BD bisect each other Given

2. AE = EC and BE = ED Definition of bisection

3. $m \angle AEB = m \angle CED$ Vertical angle theorem

Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".

4. $\Delta ABE \cong \Delta CDE$ SAS criterion for congruence

5. $m \angle ACD = m \angle CAB$ Corresponding angles of congruent triangles are congruent

6. $AB \parallel CD$ Converse of alternate interior angle theorem

7. $m \angle BEC = m \angle AED$ Vertical angle theorem

8. $\Delta BEC \cong \Delta DEA$ SAS criterion for congruence

9. $BC \parallel AD$ Converse of alternate interior angle theorem

As, $\Delta BEC \cong \Delta DEA$ , so $m \angle CBD = m \angle BDA$ as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".