Please help!

Let triangle ABC be an isosceles triangle where angle ABC is congruent to angle BCA. Prove that the sides (AB and AC) opposite the congruent base angles of a triangle are congruent.

Answers

Answer 1

I constructed line AD as a perpendicular bisector of line BC. Angles BDA and CDA are both 90 degrees because of the construction of a perpendicular bisector. Angles BDA and CDA are congruent because of the transitive property of equality.  Line BD is also equal to CD according to the definition of a perpendicular bisector. Triangles ABD and ACD are congruent by the angle side angle postulate. Since the parts of the congruent triangles are congruent, lines AB and AC are congruent.

Answer 2

The sides AB and AC opposite the congruent base angles of a triangle are congruent.

What is an isosceles triangle?

An isosceles triangle is a triangle with (at least) two equal sides. A polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180°.

For the given situation,

Triangle ABC be an isosceles triangle.

∠ABC ≅ ∠BCA.

The diagram below shows an isosceles triangle ABC with AD is the perpendicular bisector of BC.

The perpendicular bisector AD divides the line BC as BD and DC.

Then, BD = DC.

We get triangles ΔADB and ΔADC,

AD = AD [∵ common side]

⇒ [tex]\angle ADB = \angle ADC=90[/tex]

Thus by ASA theorem,

The two triangles ΔADB and ΔADC are similar.

Then by CPCT theorem,

Side AB ≅ AC.

Therefore the sides AB and AC opposite the congruent base angles of a triangle are congruent.

Hence we can conclude that the sides AB and AC opposite the congruent base angles of a triangle are congruent.

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Please Help!Let Triangle ABC Be An Isosceles Triangle Where Angle ABC Is Congruent To Angle BCA. Prove

Related Questions

Write equation given linear situation

After a baby was born, he began to gain weight at a rate of 1.5 pounds per month. The
weight of the baby at birth was 10 pounds. Write an equation for W, in terms of t,
representing weight, in pounds, of the newborn baby t months after birth.

Answers

Answer:

W=1.5x+10

Step-by-step explanation:

1.5x is the rate of weight per month

10 is the constant (how much he/she weighed at birth)

W = 1.5(T) + 10 I hope this helps

Please help me if you know the correct answer, thank you

Answers

9514 1404 393

Answer:

Option 3Option 1Option 3

Step-by-step explanation:

1. The domain is the horizontal extent of the graph. The domain of the solution space extends to x=8 on the right, with x=8 not included. The appropriate description is ...

  (-∞, 8)

__

2. A suitable matrix calculator gives the solution as ...

  (2, 5, -2)

__

3. A suitable matrix calculator gives no solution. (The reduced form of the last equation is 0=1. No variable values will make this true.)

after sharing a pizza you and two friends divide the cost by three. You each owe $2.66. Explain how to round this to the nearest dime?

Answers

Answer:

Hi so you have the answer          

Say you have 1.23 if the last digit is under 5 it would be 1.20                

Now say you have 3.47 if the last digit is above 5 it would be 3.50    

If it is something like 4.45  the 5 is the last digit so it would be 4.50

Step-by-step explanation:

um hope this helped :)

Need help I am stuck, I would like to see if my work matches someone else's to check it over.

Answers

Answer:

i think its 45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

I'm pretty sure but sorry if its incorrect.

Help me please I will give Brainlyest

Answers

Answers Below

1) = 1/5

2) = 1/4

3) = 3/20

4) = 2/25

5) = 1/3

Please Brainly

Answer:

i)1/5

ii)1/2

iii)3/20

iv)1/3

Step-by-step explanation:

Just keep eliminating in all sums as we are multiplying and u will get the ans.

Pls mark me brainliest

IF x=-4 and y=6 then xy-3x=

Answers

Answer:

-12

Step-by-step explanation:

The answer is -12 because -4x6=-24, and then you add 12 to the result. -24+12=-12, so there's your answer.

A jeepney ride cost 11 pesos for the first 4 kilometers and each additional integer kilometers adds 3.50 pesos to the fare, use a piece-wise function to represent the jeepney fare in terms of the distance f(d) in kilometers.

Answers

Answer:

[tex]f(d)=\left\{ \begin{matrix} 11 & \text{for} & 0< d\leq 4 \\-3+3.5d & \text{for}& d > 4 \end[/tex]

Step-by-step explanation:

Cost of first 4 kilometers ride = 11 pesos.

So, for the first 4 km, the fair is constant i.e.

for 1 km the fare is 11 pesos,

for 2 km the fair is also 11 pesos,

similarly, for 3 km of 4 km, the fare is 11 pesos.

Hence, for the distance [tex]0\geq d\geq 4[/tex], the fair function,

[tex]f(d)=11\cdots(i)[/tex]

After 4 km, there is an increment of $ 3.50 for each kilometer.

So, the fare function up to 5 kilometers,

[tex]f(d)=11+3.5=14.5[/tex]

So, the fare function up to 6 kilometers, i.e for the distance [tex]5<d\leq6[/tex],

[tex]f(d)=11+2\times3.5=18[/tex]

This can be arranged as the fare function up to 6 km,

[tex]f(d)=11+(6-4)\times3.5=18[/tex]

Similarly, the fare function up to [tex]d[/tex] kilometer [tex](n>4)[/tex],

[tex]f(d)=11+(d-4)\times3.5[/tex]

[tex]\Rightarrrow f(d)=-3+3.5d\cdots(ii)[/tex]

Hence, from equations (i) and (ii),

[tex]f(d)=\left\{ \begin{matrix} 11 & \text{for}\; 0< d \leq 4 \\-3+3.5d & \text{for}\; d > 4 \end[/tex]

Hye Lim drank 4/3 gallons of water in 11/2 hours. At this rate, how long will it take her to drink 4 gallons of water?

Answers

Answer:

16.5 hours

Step-by-step explanation:

Here is the explanation. As Hye drinks 4/3 gallons of water in 11/2 hours, we have a constant rate. There are 12 thirds in 4, so we are trying to find how long it takes Hye to drink 12/3 gallon. In this case, 4/3x3=12/3, so we multiply 11/2 by 3 as well, which gives us 33/2 hours. 33/2 in decimal form is 16.5 hours. Hope it helps!

Answer:

33/2 hours option 2

Step-by-step explanation:

Got it correct on edge :) hope it helps

Find the measure for angle B.

Answers

Answer:

51⁰

Step-by-step explanation:

The angles are the same

i need this ASAP The line y = -1/5x + 24 and y = 5x +9 are what to each other?

Answers

Answer:

These lines are perpendicular to each other

Step-by-step explanation:

SInce ne slope is the opposite of the reciprocal of the other

-1/5  opposite of reciprocal of 5

These are perpendicular lines

PLEASE help
PLEASE ​

Answers

Answer:

7) $57.2 (Multiply 65 by 0.12. You get $7.8. Finally, subtract 7.8 from 65.)

8) $20 (Multiply 29.99 by 0.3333. Subtract 9.99 from 29)

9) $35.7 (Do the same steps as above)

10) $276.675 (Do the same steps as above)

11) The decimal form of 57% is 0.57

12) cost= c×0.57

13) $70.65

14) $25.65 was added

Why is 18:3 and 6:1 equivalent ratios

Answers

Answer:

Because if you multiply 6 three times, it comes out to be 18.

So basically, 6 x 3 = 18

To be sure, 18 ÷ 6 = 3

So, 18:3 = 6:1

18:3 and 6:1 are equivalent ratios because those are equivalent fractions.

What is the ratio?

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or   [tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Explanation;

If we get the factors of the first ratio, we will see that;

18: 6 and 3, and 18 and 1

3: 3 and 1

Hence, if we display the ratios in fractions;

18/3 = 6/1

And then we write them in factors, we will get;

3x6/3x1 = 6/1

Simplifying;

3/3 x 6/1 = 2/1 x 3/1 = 1/6

Therefore, 18:3 and 6:1 are equivalent ratios.

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50 people were asked if they had ever been to Mauritius or the Seychelles on holiday.
11 had been to Mauritius, 7 had been to the Seychelles and 35 had been to neither.
How many had been to both?​

Answers

Answer:

11 + 7 = 18. Meaning to both Islands 15 people have visited so far.

HELP ASAP I don’t get it

Answers

Answer:

-11/5

Step-by-step explanation:

In order to solve it u should open the mixed fraction ,i.e,

11/7÷-15/21

=11/7×-21/15

Cutting,

ans=-11/5

Mark me the brainliest

Answer:

Fraction: -11/5

Decimal form: -2.2

Mixed number form: -2 1/5

Step-by-step explanation:

Angle A 5x - 5 angle b = 3x + 13 what is angle b

Answers

Answer:

Step-by-step explanation:

do you mean what is c?

There was a green house. Inside the green house there was a white house. Inside the white house there was a red house. Inside the red house there were lots of babies. What is it?

Answers

Answer:

A watermelon my woman

Step-by-step explanation:

Please answer asap. Due in 10 minutes. Will give brainliest to whoever answers in the next 10 minutes. Please answer!!!
3x/1.6 = 2/1.5

Answers

Answer:

x = 0.71 and so on

Step-by-step explanation:

The stem-and-leaf plot shows the test scores of a science class. Use the plot to answer the question.
How many students scored 78?

Answers

Answer:

4 students

Step-by-step explanation:

Understanding stem-and-leaf plots

A stem and leaf plot is designed in a way to group the numbers by their values before the ones place;

i.e. 92, 100, 101, 103, 113

Charted as

9 | 2

10 | 0 1 3

11 | 3

So, with that in mind we know 78 is grouped under the 7 | # # #

stem and has the leaf of 8 which is displayed by # | # # # 8

SO,

TO SOLVE:

Count the 8's under the 7 | # # # # group

We can see that there are 4 8's under that section, and assuming that each number is representative of one students score, we can conclude that 4 students scored 78

Hope this helps,

J.M."Jamon"

     Pennsylvania State University

     Full-Time B.S.CE. Undergrad

Answer:

4 Students

Step-by-step explanation:

If you look at the four and cout how many 8 are across you will get 4!

Harold had a summer lemonade
stand where he sold small cups for
$1.25 each and large cups for $2.50
each. He made $265. If Harold sold
88 small cups, find the number of
large cups he sold.
The basketball team scored a total

Answers

Answer:

62 large cups were sold

Step-by-step explanation:

88*1.25=110

265-110=155

155/2.50=62

What restriction should be applied to y = tanx for y = arctanx to be defined?
Look at the picture below for the choices.

Answers

Answer:

its c on edge

Step-by-step explanation:

restrict the domain to (-pi/2,pi/2)

The restriction that should be applied to the function [tex]y = tanx[/tex] for [tex]tan^{-1} (x)[/tex] to be defined is option (C) restrict the domain to [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] is the correct answer.

What is graph of a function?

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).

For the given situation,

The graph below shows the functions tan(x) and arctan(x) that is tan^-1(x)

In order to have an inverse function for trigonometry, we restrict the domain of each function, so that it is one to one.

A restricted domain gives an inverse function because the graph is one to one and able to pass the horizontal line test.

Thus by restricting the domain [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] we can obtain the function [tex]tan(x)[/tex] as [tex]tan^{-1} (x)[/tex].

Hence we can conclude that the restriction that should be applied to the function [tex]y = tanx[/tex] for [tex]tan^{-1} (x)[/tex] to be defined is option (C) restrict the domain to [tex](-\frac{\pi }{2} ,\frac{\pi }{2} )[/tex] is the correct answer.

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whats 8 more than the product of X and 8

Answers

Answer:

8X +8

Step-by-step explanation:

I believe the answer is 8x+8

Solve the inequality: -2x + 5 ≥ 3x + 20
A) x ≤ 15
B) x ≤ 3
C) x ≥ 3
D) x ≤ -3

Answers

Answer:

D) [tex]x \leqslant - 3[/tex]

Explanation provided above.

The solution to the inequality -2x + 5 ≥ 3x + 20 is x ≤ -3.

Option D is the correct answer.

We have,

To solve the inequality -2x + 5 ≥ 3x + 20, we can follow these steps:

Subtract 3x from both sides to isolate the variable on one side:

-2x - 3x + 5 ≥ 3x - 3x + 20,

-5x + 5 ≥ 20.

Subtract 5 from both sides:

-5x + 5 - 5 ≥ 20 - 5,

-5x ≥ 15.

Divide both sides by -5.

Remember that when dividing by a negative number, the inequality direction flips:

(-5x) / (-5) ≤ 15 / (-5),

x ≤ -3.

Therefore,

The solution to the inequality -2x + 5 ≥ 3x + 20 is x ≤ -3.

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5. Solve for x using the model below* Enter your answer as a number

Answers

Answer:

Step-by-step explanation:

Each triangle = - x

There are 4 of them

They equal -4x

The circles all = 1

There are 3 circles on the left

They equal 3*1 = 3

There are eleven circles on the right.

-4x + 3 = 11             Subtract 3

-4x/-4 = 8               Divide by - 4

x = 8/-4

x = -2

evaluate the expression when x=3:5x+12​

Answers

Substitute in 3 for X

5*3=15

15+12=27

27 is the answer

Answer:

27

Step-by-step explanation:

5(3)=15 +12 = 27

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the
number of tests on the y-axis and the time in weeks on the x-axis?

А. 3/4
B. 4/3
C. 3
D. 4

Answers

Answer:

i think it would be 4 i'm not sure tell me if i'm wrong.

Answer:

a

Step-by-step explanation:

If m∠1 equals (4x + 2) and m∠3 equals (5x − 25), what is the value of x?

Answers

Step-by-step explanation: the answer is x = 1/2

The value of x is 27 units.

It is required to find the value of x.

What is angle?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

If m∠1 equals (4x + 2) and m∠3 equals (5x − 25),

According to given question we have,

m∠1 =m∠3

(4x + 2)=(5x − 25)

compare the like terms and simplify we get,

2+25=5x-4x

27=x

Therefore, the value of x is 27 units.

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How do u know wether two quantities x and y are proportional

Answers

Answer:

How do u know wether two quantities x and y are proportional?

Step-by-step explanation:

Every sum x + y is the same for related pairs of x and y.

I hope that helped, let me know if you need help with anything else.

Given a linear equation in the form y=mx+b, what are the values of the slope and y-intercept of the equation?(1 point) The slope is m, and the y-intercept is y. The slope is x, and the y-intercept is b. The slope is b, and the y-intercept is m. The slope is m, and the y-intercept is b.

Answers

Answer:

The slope is m, and the y-intercept is b.

Step-by-step explanation:

What ever is attached to the x is the slope. The y-intercept is the b because it has a 0 on the x axis and a number on the y axis.

4. Stella is running in the 90 meter dash at her school track meet. If her speed is
6 meters/second, how long will it take her to run 90 meters?

Answers

It would take her about 15 seconds

Which figure represents an undefined term?
A line extends right and up from point X through point Y with an arrow instead of an endpoint.
A line connects point X and point Y.
A line extends right and up from point X through point Y with an arrow instead of an endpoint. A line extends right and down from point X through point W with an arrow instead of an endpoint.
A line extends both directs between point X and point Y.

Answers

The undefined term should be considered when A line extends both directs between point X and point Y.

What is an undefined term?

In terms of geometry, the undefined term should represent the main object where the rest of the objects should be considered as the line, point, and the plane.

So when there is the line extension that lies between point x and point Y so it should be an undefined term.

Learn more about line here: https://brainly.com/question/2037439

Answer:

Option D

Step-by-step explanation:

yes

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