When are triangles considered similar?
When are triangles considered similar? - 1

Answers

Answer 1
Answer:

If two pairs of complementary angles in a pair of triangles are congruent, then the triangles are identical. We know this because if two angle pairs are exact, then the third pair must also be equivalent. When the three angle pairs are all identical, the three pairs of sides must even be in proportion.

A triangle considered similar

Two triangles are exact if they meet one of the subsequent criteria.  

  • Two pairs of corresponding angles are equal.
  • Three pairs of corresponding sides are proportional.
  • Two pairs of corresponding sides are proportional and the corresponding angles between them are equivalent.

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Answer 2
Answer: When they are directly proportional,  are the same type (such as two equilaterals),  or have common angle lengths!

Related Questions

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HELP!!! Using a directrix of y = 2 and a focus of (3, −4), what quadratic function is created?
How do you can you solve this problem 37 + y = 87; y =

#5.Chose one of two tables below to create your own Question (with solution).

My Conditional Frequency Question is:

My solution (work and answer):

Please explain how/why you chose this question

Answers

Therefore , the solution of the given problem of unitary method comes out to be the likelihood that a particular child has a curfew given that they have tasks is 3/7, or roughly 0.43.

What is an unitary method?

The job can be completed by bringing together what was learned and applying this variable technique, that also includes all supplementary data from two people that utilized a specific tactic. To put it another way, if the desired outcome materialises, either the entity stated in the calculation will be recognised, or both expression essential processes will truly skip the colour. For forty pencils, a refundable charge of Rupees ($1.01) might be required.

Here,

Using the following formula, one can determine the conditional chance that a child will have a curfew if they have chores:

Curfew and duties are equal, so

=>P(curfew | chores) = P (chores)

The odds are listed in the table below:

=> Curfew and errands P = 3/10

=> P(tasks) = 7/9

Therefore,

=> P(curfew | chores)=3/10/ (7/10)=3/7

Therefore, the likelihood that a particular child has a curfew given that they have tasks is 3/7, or roughly 0.43.

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A student skipped a step when she tried to convert 18 hours into seconds, and she got the following incorrect result:18 hours (60 seconds/ 1 minute) = 1080 seconds

What conversion ratio did she skip in this multiple-step conversion?

A. 60 seconds/ 1 minute

B. 1 minute/ 60 seconds

C. 1 hour/ 60 minutes

D. 60 minutes/ 1 hour

Answers

Answer:

The conversion ratio that student skipped was:

D. (60 minutes/1 hour)

Step-by-step explanation:

We have to convert 18 hours into seconds

We know that there are 60 seconds in a minute and 60 minutes in an hour.

So, 1 hour= 60×60 seconds

 18 hour= 18×60×60 seconds

In the question student converted 1 minute into 60 seconds but forgot to convert 1 hour into 60 minutes

Hence, the conversion ratio that student skipped was:

D. (60 minutes/1 hour)

Answer: 60 minutes/1 hour

Step-by-step explanation: took the quiz

Jimmy is going to pack his backpack for a trip. His backpack is 60 cubic litres. He has a pile of equipment that takes up 43 cubic litres and then he has his sleeping bag that takes up 23 cubic litres. Let r be the amount of room left in his backpack. Which equation could you use to determine if he has enough room in his backpack.

Answers

Answer:

r = R - ( 43 + 23 )

There is no more space in his backpack.

Step-by-step explanation:

Jimmy's backpack has a space of 60 cubic liters (R).

Now, he has a pile of equipment of volume 43 cubic liters and then he has his sleeping bag of volume 23 cubic liters.

Now, if r is the amount of room left in his backpack, the equation I can use

r = R - ( 43 + 23 ) ....... (1) to determine if he has enough room in his backpack.

Now, in our case R = 60 cubic liters

Therefore, from equation (1), we get r = 60 - ( 43 + 23 ) = - 6, i.e. there is no more space in his backpack. (Answer)

I'm looking at the top at 79.9 angle. I'm 100ft away. What's the height of the building?

Answers

To solve this, notice that you have the angle component (I will call this a) and the x-component (the distance of you from the building) of a trig formula, and you are looking for the y-component. We will use the tangent formula, since this incorporates the angle, x, and y components.

1. Write the formula

tan(a) = y ÷ x

2. Rewrite to include the known values.

tan(79.9) = y ÷ 100

3. Solve for the unknown variable, y.

tan(79.9) × 100 = y ÷ 100 × 100

tan(79.9) × 100 = y

4. A fancy step that I call the "flip flop."

y = tan(79.9) × 100

5. Use a calculator to find the value (make sure the calculator is in "degree" and not "radians" mode).

y = 561.3968

6. Round the number as is appropriate for this problem.

Have a great day!

so this is a trig problem

so you have a right triangle
base=100 ft
from wher you are standing, it is a 79.9 angle to the top
we want to find the height of the tower or the opposite side
the base is  the adjacent side so you are looking for o/a or tan(79.9) since you know one of the sides so therefor
tan(79.9)=h/100
evaluate tan(79.9)
tan(79.9)=5.61396
5.61396=h/100
multiply both sides by 100
561.396=h
round to tenths place
561.4
the height=561.4 ft

Circle R has a radius of 6, and QP is tangent to circle R at point Q. Also, QP = 8. (a) What is the measure of ∠RQP ? Explain your answer. (b) What is the length of RP ? Explain your answer. (c) What is the length of RS ? Explain your answer. (d) What is the length of SP ? Explain your answer.

Answers

RQ = 6; RS = 6 ; these are radius

The triangle formed is right triangle. ∠RQP = 90°

QP = 8 ; this is the long leg.
RQ = 6; this is the short leg
RP = ? is the hypotenuse

a² + b² = c²
8² + 6² = c²
64 + 36 = c²
100 = c²
10 = c

The hypotenuse is 10, but RS is part of the hypotenuse, it has a measure of 6.

6 + x = 10
x = 10 - 6
x = 4   length of SP


Which of the following integrals cannot be evaluated using a simple substitution? (4 points) Select one: a. the integral of the square root of the quantity x minus 1, dx
b. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
c. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
d. the integral of x times the square root of the quantity x squared minus 1, dx

Answers

Answer:

B. and C.

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

Integration

  • Integrals
  • Indefinite Integrals
  • Integration Constant C

U-Substitution

Step-by-step explanation:

*Note:

It seems like B and C are both the same answer.

Let's define our answer choices:

a.  \displaystyle \int {√(x - 1)} \, dx

b.  \displaystyle \int {(1)/(√(1 - x^2))} \, dx

c.  \displaystyle \int {(1)/(√(1 - x^2))} \, dx

d.  \displaystyle \int {x√(x^2 - 1)} \, dx

Let's run u-substitution through each of the answer choices:

a.  \displaystyle u = x - 1 \rightarrow du = dx \ \checkmark

∴ answer choice A can be evaluated with a simple substitution.

b.  \displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice B cannot be evaluated using a simple substitution.

C.  \displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice C cannot be evaluated using a simple substitution.

D.  \displaystyle u = x^2 - 1 \rightarrow du = 2x \ dx \ \checkmark

Using a little rewriting and integration properties, this integral can be evaluated using a simple substitution.

∴ answer choice D can be evaluated using a simple substitution.

Out of all the choices, we see that B and C cannot be evaluated using a simple substitution.

∴ our answer choices should be B and C.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e