Are the triangles congruent if they are which theorem and why?

Mathematics

1 answer:

leonid [27]3 years ago

7 0

Yes the sides are equal to each other

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UNO [17]

I’m pretty sure they played 25 games.

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3 years ago

The area of a rectangle is expressed as x4 - 9y2. What are the possible dimensions of the rectangle?

AnnyKZ [126]

This is a stupid question. The teacher who asked this needs to go back to school.

A = x⁴ - 9y²

That's going to be a number. As long as it's positive we can choose any length for our rectangle L and we can compute the width by W=A/L. So the correct answer is the dimensions are L by (x⁴ - 9y²)/L.

They don't want the correct answer. They want you to factor this expression. We'll do it, but don't believe for a second this factoring somehow constrains the possible dimensions of some rectangle.

We use the difference of two squares, a²-b² = (a+b)(a-b)

A = x⁴ - 9y² = (x²)² - (3y)² = (x²+3y)(x²-3y)

Answer: x²+3y by x²-3y

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3 years ago

What does 1,580÷25=I know the answer, I need to show how I got it.

ziro4ka [17]

$\begin{gathered} \sqrt[25]{1580} \\ 1\text{ and 15 cannot divide 25 therefore, we use the first three numbers to divide 25} \\ \frac{158}{25}\text{ = }6\text{ remainder 8} \\ \text{You have to carry that remainder which is 8 and combine it with the 0 in 1580.} \\ \frac{80}{25}\text{ = }3\text{ remainder 5} \\ The\text{ remainder 5 will also divide 25} \\ \frac{5}{25}=0.2 \\ The\text{ quotient values are 63 + 0.2 = 63.2} \end{gathered}$

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The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent: Parallelogram ABC

Studentka2010 [4]

General Idea:

The angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. The theorem says that when the lines are parallel, that the alternate interior angles are equal.

Applying the concept:

Angles PBC and BAD are congruent by the <u>Corresponding Angle Theorem</u>.

Angles ABC and BAT are congruent by the <u>Alternate Interior angle Theorem</u>.