Given that △ABC is an isosceles triangle with AB⎯⎯⎯⎯⎯≅AC⎯⎯⎯⎯⎯ and AD⎯⎯⎯⎯⎯ bisecting ∠BAC, which of the following proves that ∠ABD≅∠ACD?

Answers

Answer 1

The isosceles triangle having an angle bisector [tex]\overline{AD}[/tex] forms two congruent triangles.

ΔBAD ≅ ΔCAD, therefore, ∠ABD ≅ ΔBAD, by CPCTC

Reasons:

The given parameters are;

ΔABC is an isosceles triangle.

[tex]\overline{AB}[/tex] ≅ [tex]\overline{AC}[/tex]

[tex]\overline{AD}[/tex] bisects ∠BAC

Therefore, the proof that ∠ABD  ≅ ∠ACD is given as follows;

1. [tex]\overline{AB}[/tex] ≅ [tex]\mathbf{\overline{AC}}[/tex] (Given)

2. [tex]\overline{AD}[/tex] bisects ∠BAC (Given)

3. ∠BAD ≅ ∠CAD (Definition of angle bisector)

4. [tex]\overline{AD}[/tex] ≅ [tex]\mathbf{\overline{AD}}[/tex] (Reflexive property of congruency)

5. ΔBAD ≅ ΔCAD (Side Angle Side, SAS rule of congruency based on steps 1, 3 and 4)

6. ∠ABD ≅ ∠ACD (Congruent Parts of Congruent Triangle are Congruent, CPCTC)

Learn more about SAS rule of congruency here:

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Given That ABC Is An Isosceles Triangle With ABAC And AD Bisecting BAC, Which Of The Following Proves

Related Questions

Convert this improper fraction to a Mixed Number 40/10 plz i need help

Answers

Answer:

4

Step-by-step explanation:

How many times does the denominator go into the numerator, in this case 10 goes into 40 4 times.

а 5. Protein Bar A has 15 grams of protein in
a 40 gram bar. Protein Bar B has 20 grams of protein in a 60 gram bar. Which bar has more protein per gram?​

Answers

The answer is Protein Bar A

a quter of 30 is=
pleas help

Answers

Answer:

7.5

Step-by-step explanation:

If 'quter' is quarter, then 30(1/4) is 7.5

A quarter of 30 is 7.5

All you gotta do is divided 30 by 4 cause a quarter is half of the half. It's the 1/4th part of the whole.

What addition statement does this show?



A. 5.2 + 6.4 = –11.6
B. –5.2 + 6.4 = –11.6
C. 5.2 + (–6.4) = –11.6
D. –5.2 + (–6.4) = –11.6

Answers

Answer:

D. –5.2 + (–6.4) = –11.6

Step-by-step explanation:

First, you can eliminate A and C because 5.2 is positive. Since the red arrow is pointing left, it indicates that the number (-5.2) is negative.

Then, you look at the second arrow, the green one. It is pointing left, so it would be -6.4.

I hope this helps :)

plz help me find this answer offering 10 points for a answer !!

Answers

6a and 8a 4b and 2b. hope this helps

BRAINLIEST
Do one of the above and show your work

Answers

Answer:

10,   C = circumference = 2 pi 11 = 69.11 since the radius = 6

PR = C / 2 = 34.6  since PR is 1/2 the circumference

PS = 34.6 - 16 = 18.6    since PS is 16 ft short of C/2

Answer:

Step-by-step explanation:

Can someone pls help me like plsssssssss

Answers

Answer:

2x-8

Step-by-step explanation:

hi

hope it helps you

thank me later

carryonlearing

Answer:

The third one is not the same (2+x-4)

Step-by-step explanation:

2x-8 is the same as -8+2x as it just switched places

With 2(x-4)

You multiply 2 with x and -4

Which is 2x-8

Thus the same

2+x-4

is not the same since if you add 2 and -4

You will get

x-2

Which is not the same as 2x-8

Hope this helps!

simplify
answer it
b)​

Answers

Answer:

a) 8x + 5x = 13x

b) 9f + 10f - 12f = 7f

Step-by-step explanation:

For part b, just solve from left to right normally, since adding and subtracting are inverse operations. (Inverse operation; meaning they are opposites of each other.)

So 9 + 10 = 19, and 19 - 12 = 7.

Hope this helps you :)

Step-by-step explanation:

(a) 8x + 5x = 13x....simplified

(b) 9f + 10f - 12f = 7f.....simplified

Hope it helps you!

for each fraction below find an equivalent fraction with a denominator 200.

fraction 14/25​

Answers

Answer:

112/200

Step-by-step explanation:

To find an equivalent fraction with a new denominator you can simply multiply by 1. However, you must multiply by different forms of 1. Remember that any number divided by itself is equal to 1. Additionally, because of the identity property of multiplication, any number multiplied by 1 is still equivalent.

In this case, you should multiply by a fraction that will make 25=200. To get 200 from 25 you must multiply by 8. So, multiply the whole fraction by 8/8. This gives you (14/25)*(8/8)=112/200.

A motorcycle can run 108km in 2h20mn Find the average speed

Answers

Answer:

do it got a picture

on the edge2020

Step-by-step explanation:

Helpppppppppp assssaaaap

Answers

Answer:  250

==================================================

Explanation:

x = speed of the plane in mph

x-180 = speed of the car, since its 180 mph slower than the plane

For the plane, we can form the equation

distance = rate*time

d = r*t

500 = xt

t = 500/x

For the car, we can say,

d = rt

140 = (x-180)t

140 = (x-180)*(500/x)

140x = 500(x-180)

140x = 500x - 90,000

140x - 500x = -90,000

-360x = -90,000

x = (-90,000)/(-360)

x = 250

The speed of the plane is 250 mph

-----------------------------

Extra info:

The car's speed is x-180 = 250-180 = 70 mph

It takes the plane t = d/r = 500/250 = 2 hours and it takes the car t = d/r = 140/70 = 2 hours. Both vehicles travel for 2 hours, which helps to confirm the answer.

Which number is an integer? Negative three-fourths 0 2. 3 Pi.

Answers

The number that is an integer is 0.

An integer is a number that does not have fractions or decimals. Examples of integers are 50, - 1. A fraction is a number that is made up of numerators and denominators. An example is 3/4. A decimal is made up of tenths, hundredths and thousandths. An example is 2.3.

Negative three-fourths is not an integer because it is a fraction. 2.3 and pi  is not an integer because it is a decimal.

A similar question was answered here: https://brainly.com/question/15984496

How many solutions does this system of equations have?


Exactly one

None

Infinitely many

Exactly two

Answers

Answer:

Infinitely many

Step-by-step explanation:

Write an EQUATION with an undefined slope:

Answers

Answer:

Example of an equation with an undefined slope: x = 2

Step-by-step explanation:

Definitions

The standard form of linear equations with an undefined slope is x = a, whose graph represents a vertical line. The value of a in the standard form is the x-intercept, (a, 0).  

The slope is the ratio of the vertical change in y-values to the horizontal change in x-values.

[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}}[/tex]

The slope of a vertical line is undefined because if we were to solve its slope, the denominator will be zero. As we know, division by zero is an undefined operation.  

Example:

For example, suppose that we have the following points (2, 5) (2, 10).

Let (x₁, y₁) = (2, 5)

     (x₂, y₂) = (2, 10)

Substitute these values into the slope formula:

[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{10\:-\:5}{2\:-\:2}\:=\frac{5}{0}}[/tex]

Dividing the numerator, 5, by the denominator, 0, will have an undefined quotient.

Thus, the equation of the vertical line will be: x = 2, where a = 2.

how to find r in a geometric sequence calculator

Answers

Step-by-step explanation:

We can find r by dividing the second term of the series by the first. Substitute values for a 1 , r , a n d n \displaystyle {a}_{1}, r, \text{and} n a1,r,andn into the formula and simplify. Find a1 by substituting k = 1 \displaystyle k=1 k=1 into the given explicit formula.

Given: triangle JKN J (3,1), K (5,2), N (1,5)
(all 3 need separate answers)
a) find the coordinates of the centroid.
b) find the coordinates of the orthocenter.
c) find the coordinates of the circumcenter and length of radius of circumscribed circle.

Answers

Answer:

Let the radius of the circumscribed circle be r.

The formula for calculating the radius r is

r

=

Δ

s

Where  

Δ

is the area of the triangle

s

is the semi-perimeter.

s

for any triangle is calculated as

s

=

a

+

b

+

c

3

Where,  

a

,

b

,

c

is the sides of the triangle

Δ

=

s

(

s

a

)

(

s

b

)

(

s

c

)

(Heron's Formula)

Plug in the values and get the answer.

Once you have the radius, you can easily find out the area of the circle.

Step-by-step explanation:

Monty Ricker obtained a used car loan of $6,000.00 at 8% for 36 months. The monthly payment is $ 187.80. The balance of the loan after 12 payments is $ 4,159.90. The balance after the 34th payment is $ 380.60.

Answers

Answer:

What is the intrest for the 13th payment?

Answer:  What is the interset

Step-by-step explanation:

PLS HELP ME I DON'T GET IT

Answers

Answer:

  (a) $14,912 saved

  (b) $58,000 aid needed

Step-by-step explanation:

(a)

Nola is saving $200 each month. That means she will have saved 60 times that amount after 60 months:

  60 × $200 = $12,000

When she adds that to her current savings she will have saved a total of ...

  $12,000 +2,912 = $14,912 . . . by the time she starts college

__

(b)

The figure is telling you Nola will need $72,912 for 4 years of college. If she funds $14,912 from her own savings, then she will need an additional amount of ...

  $72,912 -14,912 = $58,000 . . . . amount of financial aid needed

nolan is taking a multiple choice test his grade is given by the equation y=70-2x where y represents his final score and x represents the number of questions he got wrong . waht could the number 70 represents in the equation? ​

Answers

Answer:

70 could represent the total number of points nolan can earn on the test

Step-by-step explanation:

A store manager predicts that 100 hats will be sold if each hat costs $12. The manager predicts that 4 less hats will be sond for every $1 increase in price. For what prices can the manager predict that 60 hats will be sold?

Answers

Answer:

100-60=40

40/4=10

10*$1=$10

$12+$10=$22

what is the area of a hexagon inscribed in a circle with a diameter of 8

Answers

Answer:

the side = the radius for a hexagon.

so, area = 6 times the area of one equilateral triangle of side 4.

Juliet needs to rewrite 3 (x 2) = 6 y in slope-intercept form so she can easily graph it. Which step would be correct to start the process? She could combine the x and 2 to get 3 (2 x) = 6 y. She could divide both sides by 3 to get x 2 = 2 y. She could distribute the 3 to get 3 x 2 = 6 y. She could subtract the 6y to get Negative 6 y = 3 (x 2).

Answers

The step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y

Note that the standard equation of a line in slope-intercept form is expressed as y = mx + b

m is the slopeb is the y-intercept

Given the function 3(x+2)=6y, for Juliet to write in slope-intercept form, the best approach is to first divide both equations by 6 as shown:

[tex]3(x+2)=6y \\\frac{3(x+2)}{6} =\frac{6y}{6} \\\frac{x+2}{6}=y[/tex]

Swap sides

[tex]y=\frac{x+2}{6}\\y=\frac{1}{6}x +\frac{1}{3}[/tex]

She could as well distribute the 3 over x + 2 to have:

3(x + 2) = 6y

3x + 3(2) = 6y

3x + 6 = 6y

Hence based on the option, the step that would be correct to start the process is she could distribute the 3 to get 3x+2=6y

Learn more on distributive law here: https://brainly.com/question/25224410

Answer:

Its C

Nevermind Its Not its A or B

Step-by-step explanation:

:)

what is equivelent to 4x+(2x+4)?

Answers

Answer:

8x + 16

Step-by-step explanation:

4x times 2x = 8x

4 times 4 = 16

8x + 16

YW!!!

Answer:

The solution is 6x+4

Step-by-step explanation:

4x+(2x+4)

= 4x+2x+4

= 6x+4

in the parentheses we lose it because it is added instead of multiplied

The teacher collected some snowfall data during one of the snow days last year. Estimate the total snowfall throughout the day.

Answers

The total snowfall throughout the day is the expected value of the distribution.

The estimated total snowfall during the day is 30 inches

Start by calculating the average rate of snow collected on that day.

[tex]Rate = \frac{0 + 1.5 + 2.5 + 2.0 +1.0 +0.5}{6}[/tex]

This gives

[tex]Rate = \frac{7.5}{6}[/tex]

Divide 7.5 by 6

[tex]Rate = 1.25[/tex]

There are 24 hours in a day.

So, the total snowfall is:

[tex]Total = Rate \times Hours[/tex]

This gives

[tex]Total = 1.25 \times 24[/tex]

Multiply

[tex]Total = 30[/tex]

Hence, the estimated total snowfall during the day is 30 inches

Read more about expected values at:

https://brainly.com/question/13005177

CAN SOMEONE HELP ME PLEASE ASAP!?

Answers

if u can get a better picture I can help you

To reach the roof , how far away from the building should he place the base of the ladder ?

Answers

Answer: many be 5-10 feet

So far, Charlie has pures 456.6 Glories. He wants to burn a total of 500 calorierHow many more calories must Charlie burn?
| 0
2

Answers

Well if he’s burned 456.6 calories already and he needs to get to 500 then you would have to simply subtract 456.6 from 500
The equation: 500 - 456.6 = 43.4
Hope this helps!

How do I factor this problem?

Answers

Answer = 16x(3x-1) . Hope it helps.

List the factors for 48 and -16 and find the greatest common factor .

48= 1 ,48

2, 24

4, 12

6, 8

16 = 1,16

2,8

4, 4

The Greatest common factor between these two is 8. Because they have a 8 in common.

8(6x^2-2x)

Why does demand for a product or service play a significant role in starting a new business?

Answers

Answer:

Basic economics like demand should important to you whether you run a seasonal business, buy a vacation property for passive income, or run a more traditional firm.

what is the relationship between the amplitude of light of light waves and brightness

Answers

Answer: The amplitude of light waves is associated with our experience of brightness or intensity of color, with larger amplitudes appearing brighter.

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