All categories

3 years ago

What do you need to show to prove two triangles are similar by SAS Similarity Theorem?

2 answers:

7 0

Two triangles are similar by SAS similarity if they have two sides in the same ratio and the angles between those sides in both triangles are equal.

V125BC [204]3 years ago

4 0

You need to show that two sides of one triangle are proportional to two corresponding sides of another triangle, with the included corresponding angles being congruent.

You might be interested in

Find the volume and area for the objects shown and answer Question

klio [65]

Step-by-step explanation:

You must write formulas regarding the volume and surface area of the given solids.

$\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2$

$\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\$

$\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}$

$\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}$

$SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}$

6 0

3 years ago

A truck spilled 1000 gallons of asphalt on the 5 freeway. Come up with a way to approximate the cost of the clean up

Genrish500 [490]

I subway yahquissiisn

6 0

3 years ago

Deron is making light switch plate from pieces of wood. He starts with a board that is 6 yards long. How many light switch plate

Mazyrski [523]

Is there more to this question

4 0

3 years ago

Evaluate the expression 3 4/5x-2 1/2 for x =-10

lyudmila [28]

Answer:

The value of given expression for x = - 10 is - 81

Step-by-step explanation:

Given expression as :

3 $\frac{4}{5}$ x - 2 $\frac{1}{2}$

Or, 3 + $\frac{4}{5}$ x - 2 - $\frac{1}{2}$

Or, $\frac{19}{5}$ x - $\frac{5}{2}$

or, $\frac{38 x - 25}{5}$

Now for x = - 10

$\frac{38\times (- 10) - 25}{5}$

Or, ${38\times (- 2) - 5}$

∴ - 76 - 5

Or, - 81

Hence The value of given expression for x = - 10 is - 81 Answer

5 0

3 years ago

Which of the following expressions is equal to 5 - 2m?

r-ruslan [8.4K]

Alright, I'm pretty sure I can help.

Let's look at the first answer choice.

7 - 2 (m + 1)

Distribute -2 and add the remaining numbers to get the total for that answer choice.

7 - 2m - 2

Simplify. You get 5 - 2m.

Looks like we found the answer on the first choice!

The Final Answer is 7 - 2 (m + 1)

7 0

3 years ago

Read 2 more answers