Tuesday, December 5, 2023

# Find The Value Of Each Variable Geometry

## To Calculate: To Find The Value Of Each Variable In The Given Parallelogram

Find the values of the variables x and y given figures and congruent angles

The values of variables are x

Since opposite sides of parallelogram are equal,

Thus,

Also, consecutive sides of parallelogram are supplementary,

Thus,

On solving the above equation:

Hence, Value of variables are x

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## How To Graph Variables In Algebra

Once you know the value of a variable, you can graph it since all numbers can be graphed on a number line. Just locate the value on the number line and put a dot.

For example, graphing x = 4 gives the following graph:

Other examples:

Graph x = -6 on the number line.

Just locate -6 on the number line and draw a circle at -6.

Graph x = 0

Just locate 0 on the number line and draw a circle.

Now, write a statement of equality for each of the following graphs. Use x as the variable.

Graph #1:

## How To Find The Value Of A Variable In Geometry

Variables, or unknown values, appear in numerous types of equations from simple algebra problems to complex calculus problems. In geometry, variables often appear in problems related to perimeter, area and volume. Typical problems provide you with some precise measurements and ask you to find out an unknown measurement, or variable.

Determine which formula you need. For example, if you’re working with the area of a triangle, you need to know that area equals one half the base times the height, or A=1/2bh.

Plug the known values into the formula. Using the area of the triangle example, assume you know that the area is 100 square inches and the base is 20 inches. When you plug these values into the formula, you get 100=1/2 . The height of the triangle is the variable.

Use the order of operations in reverse to isolate the variable on one side of the equation. The order of operations is PEMDAS — parentheses, exponents, multiplication, division, addition and subtraction. When solving for a variable, use the order in reverse — SADMEP.

Perform the opposite operation to what is called for in the equation. If the equation requires you to multiply, you will divide. If the equation calls for subtraction, you will add.

#### Tips

• Be sure all measurements use the same unit of measurement. If the problem gives an area in square feet and the length of side in inches, you will need to convert the feet to inches before solving the equation.

## Find The Value Of Each Variable Problem Of

• Slides: 16

Find the value of each variable. Problem of the Day

Section 4 -3 Congruent Triangles

Objectives Then Now You identified and used congruent angles. Name and use corresponding parts of congruent triangles.

Content Standards Common Core State Standards G. CO. 7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G. SRT. 5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 3) Construct viable arguments and critique the reasoning of others. 6) Attend to precision.

If two geometric figures have exactly the same shape and size, they are congruent. In two congruent polygons, all of the parts of one polygon are congruent to the corresponding parts or matching parts of the other polygon. Vocabulary These corresponding parts include corresponding angles and corresponding sides.

Definition of Congruent Polygons

Show the polygons are congruent by identifying all the congruent corresponding parts. Then write a congruence statement. Example 1

Show the polygons are congruent by identifying all the congruent corresponding parts. Then write a congruence statement. Example 1

Vocabulary Corresponding P arts of Congruent T riangles are Congruent

In the diagram, RSV TVS. Find the values of x and y. Example 2

Third Angles Theorem

Example 3

## In The Figure How Do I Find The Value Of The Variable According to the problem, I have to find the value of the variable in simplest radical form. I began with the equation 189 = 6 x, so x = 93. Now, I know we have to find the area of the base in terms of x. But how do I find the height do I use Pythagorean Theorem?

• $\begingroup$Please, if you are ok, you can accept the answer and set it as solved. Thanks!$\endgroup$

You can use Heron’s formula for example.

Or since it is an equilateral triangle by the sine formula:

$$A=\frac12x^2\sin60°=\frac$$

You can find many other formulas here Equilateral triangle.

In an equilateral triangle, the heights are exactly the medians. Whence, the heights have length:$$\frac}x.$$

Your initial equation is a little strange, it uses $x$ to designate the area of the base of the pyramid, while in fact on the picture $x$ has another meaning, which is the length of the edges of the base. Also some $\sqrt$ became $\sqrt$, but the result still good, I suspect a typo here.

I would write for a pyramid $V=\frac 13 BH\implies B=\dfracH=\dfrac}6=9\sqrt$

Note: on this picture I found on the web, they used $a$ in place of $x$.

Now the base is an equilateral triangle.

Area is $B=h\times \frac x2$

And by Pythagoras $^2+h^2=x^2$ so $h=\frac}2x$

Thus you get $B=\frac}4x^2=9\sqrt\implies x^2=36\implies x=6$

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