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3 years ago

What information is necessary to prove two triangles are similar by the SAS similarity theorem?

Mathematics

2 answers:

Irina18 [472]3 years ago

4 0

Answer:

If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Step-by-step explanation:

Airida [17]3 years ago

4 0

Answer:

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.

Step-by-step explanation:

You might be interested in

Question:

aivan3 [116]

Answer:

part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

$\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}$

The scale factor is equal to

$z=\frac{CB}{C'B'}$

substitute

$z=\frac{4}{8}$

simplify

$z=\frac{1}{2}$

Part B) What is the ratio of the areas (small to large)?

<em>Area of the small triangle</em>

$A=\frac{1}{2}(2)(4)=4\ units^2$

<em>Area of the large triangle</em>

$A=\frac{1}{2}(4)(8)=16\ units^2$

ratio of the areas (small to large)

$ratio=\frac{4}{16}=\frac{1}{4}$

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

4 0

3 years ago

What is the value of the expression below when w = 3. 4w^2 - 7w - 8

Makovka662 [10]

<h2>Answer:<em> </em><em><u>w =(-40-√4320)/-34=(20+6√ 30 )/17= 3.110 </u></em></h2><h2><em><u> w =(-40+√4320)/-34=(20-6√ 30 )/17= -0.757</u></em></h2>

Step-by-step explanation: The prime factorization of 4320 is

2•2•2•2•2•3•3•3•5

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 4320 = √ 2•2•2•2•2•3•3•3•5 =2•2•3•√ 30 =

± 12 • √ 30

√ 30 , rounded to 4 decimal digits, is 5.4772

So now we are looking at:

w = ( -40 ± 12 • 5.477 ) / -34

Two real solutions:

w =(-40+√4320)/-34=(20-6√ 30 )/17= -0.757

or:

w =(-40-√4320)/-34=(20+6√ 30 )/17= 3.110

MY HEAD HURTS!

3 0

3 years ago

The town of worman grove has collected 28,481 pens for school supplies drive. Their goal is 30,000 pens .Show how to use countin

frosja888 [35]

Answer:

1519

Step-by-step explanation:

if wrong super sooryyyyy :(

5 0

2 years ago

Solve inverse operation of A - 5/6 = - 3 2/3

gayaneshka [121]

Answer:

- 2 5/6 = A

Step-by-step explanation:

- 3 2/3 + 5/6 = A

- 2 5/6 = A

3 0

3 years ago

F(x) = 4x − 12 <br><br> f−1(x) =___? x +____?

natali 33 [55]

Answer:

$f^{-1}(x)=\frac{1}{4}x+3$

Step-by-step explanation:

We have been given the function $f(x)=4x-12$

Below are steps for finding the inverse of the function.

Step 1:

Replace f(x) with y

$y=4x-12$

Step 2:

Interchange x and y

$x=4y-12$

Step 3:

Solve for y

$x+12=4y\\\\y=\frac{1}{4}x+3$

Step 4:

Replace y with $f^{-1}(x)$

$f^{-1}(x)=\frac{1}{4}x+3$

6 0

3 years ago