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3 years ago

How are rigid transformations used to justify the SAS congruence theorem?

Mathematics

2 answers:

Yuliya22 [10]3 years ago

7 0

Rigid transformations preserve segment lengths and angle measures. If you can find a rigid transformation, or a combination of rigid transformations, to map one triangle onto the other, then the triangles are congruent. To prove SAS, we started with two distinct triangles that had a pair of congruent corresponding sides and a congruent corresponding included angle. Then we performed a translation, followed by a rotation, followed by a reflection, to map one triangle onto the other, proving the SAS congruence theorem.

Katena32 [7]3 years ago

3 0

(Refer to the diagram in the attached photo.)

In this diagram there is defined two Sides and an Angle in between (SAS).

Notice how there are two loose endpoints in the diagram. A single line segment can be drawn connecting the endpoints, forming a unique triangle.

If the original diagram is transformed, the dimensions and angles formed by the third line segment remains the same relative to the first two.

Therefore, if two triangles have the same SAS configuration, then they are congruent.

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Javier has a basket of oranges and apples. The number of oranges is 2 more than twice the number of apples in the basket. The di

Vesna [10]

Hello!

Let's put this into a system of equations and have a represent the apples and o represent the oranges.

o=2a+2
0.5o-0.5a=4

Since we can already so what o equals (2a+2) we will substitute it into the second equation and solve for a.

0.5(2a+2)-0.5a=4
1a+1-0.5a=4
1.5a+1=4
1.5a=3
a=2

Now that we know the value of a will put a into the first equation to find o.

o=2(2)+2
o=4+2
o=6

There were 6 oranges and 2 apples.

I hope this helps!

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3 years ago

In the following exercises, solve

yKpoI14uk [10]

Answer:

When the volume of a gas in a container varies inversely with the pressure on the gas and a container of nitrogen has a volume of 29.5 litres with 2000 psi. So, if the tank has a 14.7 psi pressure, then the volume of the tank would be 4013.6 litres.

Step-by-step explanation:

The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of litres with psi, what is the volume if the tank has a psi pressure.

Calculate the volume to the nearest whole number.

Use the given values and calculate the proportionality constant as well as required solution.

Step 1 of 2

Write the inversely proportionality relation between the volume and pressure of a gas in container.

$v \propto \frac{1}{p}$

Where volume is represented by v and pressure is represented by p.

Remove the proportionality and place a constant say k.

$v=\frac{k}{p}$

Substitute the given values of nitrogen that v=29.5 and

p=2000 and calculate the value of k from above equation.

$\begin{aligned}&29.5=\frac{k}{2000} \\&\Rightarrow k=29.5 \times 2000 \\&\Rightarrow k=59000\end{aligned}$

Step 2 of 2

Substitute the value p=14.7 and above calculated k value in the equation

$\begin{aligned}&v=\frac{k}{p} . \\&v=\frac{59000}{14.7} \\&\Rightarrow v=4013.6\end{aligned}$

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