ΔABC is an equilateral triangle with AD perpendicular to BC. Prove that ΔADB ≅ ΔADC.

Answers

Answer 1

Step-by-step explanation:

An equilateral triangle means all sides are congruent.

AB≅BC≅AC

All angles are also congruent.

∠ABC≅∠BCA≅∠CAB

AD being perpendicular makes it a bisector of both BC and ∠CAB.

BD≅CD

∠BAD≅∠CAD

Now, there are multiple ways to prove that ΔADB≅ΔADC. All 3 sides and all 3 angles of both triangles are congruent, so you could do it however you want.

1) ASA (one of the possible ASA combinations)

∠ABD ≅ ∠ACD because this is an equilateral triangleBD ≅ CD because AD bisects BC∠BDA ≅ ∠CDA because AD is perpendicular to BC, both 90°

2) HL (again, one of the multiple possible HL combinations)

AD is perpendicular to BC, creating 2 right trianglesAB ≅ AC because ΔABC is equilateralAD ≅ DA by the reflexive property, it is congruent to itself

There are many more but I won't write them all out.

ABC Is An Equilateral Triangle With AD Perpendicular To BC. Prove That ADB ADC.

Related Questions

Chose the graph which represents the solution to the inequality

Answers

Answer:

See answers below.

Step-by-step explanation:

 x  =  - 4x + 15             Change the ≤ to an = and solve for x    

4x =   4x          

5x  =       15

  x =    3           Now replace the equal sign with ≤

    x ≤ 3

The graph: closed circle dot at point 3 and shaded to the left . Can not see the graph but pick the one that starts at 3 and shaded to the left.

A magnifying glass shows the image of an object that is 10 times the objects actual size. Determine the length of the image of the object if the actual length of the object is 8 millimeters

Answers

The correct answer is 80 millimeters

answer asap!!
thank u :)

Answers

Answer:

I can't see the photo it's just a blank black screen.

Step-by-step explanation:

Guided Practice

Type your answer and then click or tap Done.

What is the vertex of the parabola with the equation y=15x^2+2x−8?

Answers

Answer:

(Fill in the blank text field 1

-5

, Fill in the blank text field 2

-13

)

Step-by-step explanation:

(Fill in the blank text field 1

-5

, Fill in the blank text field 2

-13

)

Done

The vertex of the parabola is (−5, −13).

Rewrite in vertex form and use this form to find the vertex  

(

h

,

k

)

.

(

1

/15

,

121

/15

)

Find the vertex form.

y

=

15

(

x

+

1

/15

)

2

121

/15

Find the value of 7u-8 given that -4u-5=3

Answers

Answer:

22

Step-by-step explanation:

-4u - 5 = 3

=> -4u = 8

=> u = -2

=> 7(-2) - 8

=> -14 - 8

=> -22

Therefore, -22 is our answer.

Hoped this helped.

Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?

Answers

Step-by-step explanation:

Given:

Lemons - l and apples - aa = 35¢, l = 15¢Number of apples and lemons = 17Cost of lemons and apples = $3.95 = 395¢

System as per question:

a + l = 1735a + 15l = 395

Or

a + l = 170.35a + 0.15l = 3.95

Step-by-step explanation:

Let the number of apples be a and lemons be l . Then ,

=> a + l = 17

Also ,

=> 35a + 15l = $ 3.95

Given the expression -2 + x + (-5) what values of x will make the expression greather than zero? Create and inequality to represent your solution

Answers

-2+x+(-5) > 0  <=> x-7 > 0 <=> x > 7

ok done. Thank to me :>

What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Cab?

Answers

Step-by-step explanation:

the general slope intercept form is

y = ax + b

a is the slope. it is expressed as ratio of y change / x change when going from one point to another.

b is the y-intercept (the point, where the line crosses the y-axis, meaning the y value when x=0).

we get b by using the point coordinates in the equation and solve for b.

we see costs is on the y axis, and miles is on the x axis.

so what points do we identify on the chart for the green taxi ?

there is right on the y-axis (0, 5). which is already our y-intercept.

and then let's pick e.g. the point where both lines intercept : (3, 8).

for the slope we look at the coordinate changes :

x changes by +3 (from 0 to 3).

y changes by +3 (from 5 to 8).

so, the slope is 3/3 = 1.

and again, the y- intercept is +5.

therefore, the line equation is

y = x + 5

meaning the cost of a fare is the number of miles plus 5.

A 98% confidence interval is found to be (32,46). What is the margin of error ?

Answers

Using confidence interval concepts, it is found that the margin of error is of 7.

A confidence interval has the format (a,b).The margin of error is half the difference between the two bounds, that is:

[tex]M = \frac{b - a}{2}[/tex]

In this problem, the interval is (32, 46), hence [tex]b = 46, a = 32[/tex], and the margin of error is:

[tex]M = \frac{46 - 32}{2} = 7[/tex]

The margin of error is of 7.

A similar problem is given at https://brainly.com/question/25704940

Answer:

Step-by-step explanation:

its 7 just did it

You are solving 5 – 8/3

=y/3
. Which equation will you get if you multiply both sides by 3?

Answers

Answer:

y=0.76

Step-by-step explanation:

5-8/3 = 3y

(5-8/3) x 3 = 3y x 3

6.9=9y

9y=6.9

y=6.9/9

y=0.76

Write the phrase as an equation /
inequality
Four is twenty more than the number.
Help pls

Answers

Answer:

4 = 20 + n, where n is the number

Step-by-step explanation:

Here are a few key words to use when converting words to an equation

"is": =

"more": +

"less": -

"more than", "greater than": >

"less than": <

N is the variable we are using here so four and twenty are the coefficients here

So the answer would be

4=20+N

Put the following equation of a line into slope-intercept form, simplifying all fractions, 6x+4y=-12

Answers

Answer:

Step-by-step explanation:

6x+4y=-12

subtract 6x from both sides in order to move 6x to the other side.

4y=-12-6x

divide 4 from the whole equation in order to make the 4y to y.

y= -3-6/4x

and to simply

y= -1.5x-3

or y= -3/2x-3

Graph the equation.

Answers

Y=10x Dats what I got sorry if wrong

A certain class has 25 students. If 8 students play football and, 10 plays baseball and 6 plays both, how many students play neither football nor baseball?

Answers

Answer:1

Step-by-step explanation:

8+10=18 18+6=24 25-24=1

Answer:

7

Step-by-step explanation:

8 fb

10 bb

6 both, but are among the 8 & 10

so 7

hope it helps

please help me with this for a brainly plus give explaantion on how you got that answer

Answers

D is the correct answer

Surface area I need help

Answers

Answer:

100 + 100 + 40 + 40 + 40 + 40 = 360 yd^3

Can someone please help me with this?

Answers

Hello,

Ali is right, Khamis is wrong. Why because Khamis forgot to put the negative sign in front of 5b, it should be wrote -5b in the second line and not 5b.

And then Khamis should have divided -5b by -5b.

Good Luck

Ali is correct
Ali is correct

3х — бу - z = 3
4х +4y +z= — 1
X-2y – z = -1

Answers

Answer:

[tex]3x - 6y - x + 3 = =[/tex]

Please help and no links

Answers

Answer:

B) y=3x

Step-by-step explanation:

2 x 3 = 6

3 x 3 = 9

4 x 3 = 12

You can find y by multiplying the x by 3. The relationship between the x and y is proportional. For example, lets say my x is 20, my y would be 60. 20 x 3 = 60.

If you are still unsure, remember constant of proportionality is k=y/x, so your constant is 3.

Please I really do need ur help. 4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number.

What is the number?

Enter your answer as a mixed number in the simplest form in the box.

Answers

The answer is 1 25/57.

Just set the question into an equation:
(2 1/3+ 5/6)x = 4 5/9
(Solve for x and you’ll get 1 25/57).

Answer:  X =  2 2/3

Step-by-step explanation:

4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number.

Let X be the "number."  Translate the sentence:

(4 5/9) = ((2 1/3) + (5/6))*X

"4 5/9 is the same":  (4 5/9) =

"as the sum of 2 1/3 and 5/6":  ((2 1/3) + (5/6))

"times a number": *X

Put them all together:

(4 5/9) = ((2 1/3) + (5/6))*X

(41/9)-(7/3) = (5/6)X

(41/9)-(21/9) = (5/6)X

(20/9) = (5/6)X

X = (20/9)*(6/5)

X = 120/45

X = 2 30/45 or 2 2/3

How to draw on the graph
y=3x
y=x-6

I need it as soon as possible plz

Answers

Answer:

I believe the graphing should look like this.

Step-by-step explanation:

SOMEONE HELP ME PLEASE

Answers

Answer:

[tex]x=\frac{27}4=6.75[/tex]

Step-by-step explanation:

The triangles PQR and SQT have corresponding angles congruent. In particular the pair P,S, R,T are congruent since corresponding angles relative to the two parallel lines in the hypotesis, and Q is obviously in common. The two triangles are similar since their angles are congruent. We can then write the follwing proportion.

[tex]\overline{RQ}:\overline {TQ}= \overline{PQ}:\overline{SQ}[/tex]  Replacing the values and cross-multiplying we get:

[tex](4x-3+3):3=(40+5):5 \rightarrow 4x:3 = 45:5 \\4x=27 \rightarrow x=\frac{27}4=6.75[/tex]

Answer:

6.75

Step-by-step explanation:

the answer is 6.75

so x = 6.75

- Andy wants to rent a one-bedroom apartment in Green Acres. The apartment has a monthly rent of
$1,425. He must pay a $150 application fee, a security deposit that is equal to one month's rent and must
also
pay the last month's rent. His broker charges 5% of the yearly rent. How much is he expected to pay
up front in order to rent this apartment?

Answers

Answer:

$161.88

Step-by-step explanation:

1, 425 * 0.05 = 71.25 = yearly

71.25 / 12 = 5.94 = monthly

5.94 * 2 = 11.88 = for two months

11.88 + 150 = 161.88 = the amount he is expected to pay

Tell me if I'm wrong :)

Which answer correctly describes the transformation from the preimage to the
image?
a translation 10 units left and 8 units down
a reflection over the x-axis

a translation 10 units right and 8 units up

a rotation of 180°

a reflection over the y-axis

Answers

Answer: Choice A

Translation of 10 units left and 8 units down

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

Explanation:

Always start with the preimage. Let's say we focus on point A located at (3,6). Its corresponding point is A' located at (-7,-2). To go from (3,6) to (-7,-2), we move 10 units to the left and 8 units down.

The motion "10 units to the left" means we subtract 10 from the x coordinate. The "8 units down" part means we subtract 8 from the y coordinate.

Overall, the translation rule is [tex](x,y) \to (x-10,y-8)[/tex]

If we applied that rule to A(3,6), then...

[tex](x,y) \to (x-10,y-8)\\\\(3,6) \to (3-10,6-8)\\\\(3,6) \to (-7,-2)\\\\[/tex]

which is what the diagram shows going from A to A'

Let's do the same for point B(3,1)

[tex](x,y) \to (x-10,y-8)\\\\(3,1) \to (3-10,1-8)\\\\(3,1) \to (-7,-7)\\\\[/tex]

This indicates B(3,1) moves to B ' (-7,-7) which is what the diagram shows. I'll let you confirm that C(6,6) moves to C ' (-4,-2) using that translation rule.

nia saw a watch on sale for 42.50 the original price of the watch was 69.95 what is the approximate discount on the watch

Answers

Answer:

0.2745%

Step-by-step explanation:

69.95-42.50=27.45

27.45×100=27.45%

Given m||n, find the value of x. (10X-40°)(x-140°​

Answers

Answer:

1

Step-by-step explanation:

no es mi culpa que eres una caca

what is the equation of the trend line in the scatter plot

Answers

Answer: y = -x + 8

When you replace x by 0, you obtain y = 8 and when you replace x by 6, you obtain 2. (the red dots on the graph)

How do you write the nth term rule for the sequence
1
,
3
,
5
,
7

Answers

basically the answer is 2n-1  2n comes from the difference to get from 1 to three and the -1 from 2n to get to 1 you need to minus 1 so you get -1

can someone help me with this please:) ​

Answers

Answer:

A

Step-by-step explanation:

[tex]2 \sqrt{3} + \sqrt{9} \times \sqrt{ - 1} = 2 \sqrt{3} + 3i[/tex]

There are 4 red marbles, 2 white marbles, and 2 black marbles in a bag. Consider the following compound events. What is the probability that marina will pick two red marbles if she returns the first marble to the bag

Answers

Answer:

8

Step-by-step explanation:

eight more anakd;odslakhas sfjjjsjas

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