Complete the following proof. Given: (BD) is the perpendicular bisector of (AC) Prove: ∢A≅∢C
Statement Reason
1. (BD) is the perpendicular bisector of (AC) 1. Given
2. Point B is the midpoint of (AC) 2. Definition of perpendicular bisector
3. 3. Definition of midpoint
4. ∢ABD and ∢CBD are right angles 4. Definition of perpendicular bisector
5. ∢ABD and ∢CBD are congruent 5. All right angles are congruent.
6. 6. Reflexive property of congruence
7. 7.
8. ∡A≅∡C 8.
Answers
Answer:
I dont know if this is right but... i tried XD
Step-by-step explanation:
Angle A is congruent to angle C.
What is Triangle?A triangle in geometry is a polygon with three sides and three angles. The sum of the interior angles of a triangle is 180°.
If XYZ is a triangle, it is represented as ΔXYZ
Here, it is given that BD is the perpendicular bisector of AC.
Then by the definition of perpendicular bisector, B is the midpoint of AC.
Consider ΔABD and ΔCBD
ΔABD and ΔCBD are right triangles with ∡ABD = ∡CBD = 90°.
So, ∡ABD ≅ ∡CBD (∵ all right angles are congruent)
Now, by the reflexive property of congruence, every side or angles are congruent to itself.
So BD ≅ BD
Since B is the midpoint of AC, AB = BC.
Hence AB ≅ BC
By SAS theorem, if two sides and an angle of a triangle are congruent to two sides and angles of another triangle, then both triangles are congruent.
Hence ΔABD ≅ ΔCBD
So, Angle A is congruent to angle C.
Hence ∡A ≅ ∡C if BD is perpendicular bisector of AC.
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Related Questions
Pls help me on this
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Answer:
I don't understand anything. if I was know of course I will help you
3 times a Numbers plus 12 is more than 15?
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Answer:
2,3,4,5,6,7,8,9 etc
Step-by-step explanation:
Answer:
3x + 12 > 15
this can be simplified to
x > 1
Step-by-step explanation:
:D
I already Have the answer but can u guys show the work?
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…………..
PLZZ HELP EMMMM!!!!
!!!!!!!!!!!!!!
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[tex]-2[/tex] is a less of a loss than [tex]-5[/tex], but a lost of [tex]5[/tex] points is a greater loss than of [tex]2[/tex] points
How do you Find cross products with multiplication?
I will give 500 pts and Brainliest!
Answers
Answer:
A cross product is an form from an vector multiplication, performed in between for two vectors from a different kinds or nature. An vector may have both magnitude also direction. So we can multiply two or more vectors for crossing a product also a dot product. The resultant vector is an perpendicular to a plane having the two add vectors.
Step-by-step explanation:
Sorry if I am wrong!!!!Answer:
between for two vectors from a different kinds or nature. i think
brainliest???
Step-by-step explanation:
OABD is a sector of a circle.
Angle AOB = 80°.
The radius OB = 22 cm.
Work out:
the length OC
The area of triangle OAB
The area of the sector OABD
The area if the segment ABD
Answers
90
Step-by-step explanation:
because it has a parallel line
please explain and answer it
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8√21 cm² is the area
hope it helps you
please mark as brainlliest!!
Graph the lines y=3x+3
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~graph
Graph the line using the slope and y-intercept, or two points.
Slope : 3
y intercept = (0 , 3)
graph already attached ✔️
~ nice to help you ^^
Answer:
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!8
Answers
Answer:
Step-by-step explanation:
y - 4 = -2(x - 6) It might be easier to do if we removed the brackets and collect like terms.
y - 4 = -2x + 12 Add 4 to both sides
y = - 2x + 4 + 12 Combine
y = - 2x + 16
It's not one because -6*-2 + 16 = 28 for y.
It's B
y = -2 * 6 + 16
y = - 12 + 16
y = 4
(6,4) is the answer.
c: doesn't appear to be right. Any minus sign is going to make the number in front of x + which only adds to 16 making bigger.
d: -2*4 + 16 = - 8 + 16 = 8 which is incorrect. The answer should by 6 not 8
How many sides do 1 quadrilateral, 5 hexagons, and 1 heptagon have in all?
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Answer:
Pentagon - 5 sides = 5 x 4 = 20
Hexagon - 6 sides = 6 x 5 = 30
Nanagon - 9 sides = 9
20 + 30 + 9 = 59 IN TOTAL
Step-by-step explanation:
If the vertical length is 10, what is the horizontal length?
Answers
Answer:
5
Step-by-step explanation:
it is half of ten which is 5
Hope this helps
Answer:
top one is correct I think
what is the volume of the prism ?
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Answer:
Your answer is 150 units!
round 6,311 to the nearest thousand
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Answer:
6,000
Step-by-step explanation:
solve pls brainliest
Answers
A youth group went on trip to EXPO Dubai Travelling in two Vans. The number of people in each van and the total cost of admission are shown in the table. Find the adult price and student price of admission
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Answer:
Refer to the attachment
Soo :
2a + 3b = 325
2a + 7b = 505 -
-4b = -180
4b = 180
b = 45
[tex] \: [/tex]
2a + 3b = 325
2a + 3(45) = 325
2a + 135 = 325
2a = 325 - 135
2a = 190
a = 95
Find the value of x. Th angles on a triangle .Please explain your method.
Answers
The internal values of all triangles are worth 180°, so knowing this, just form a 1st degree equation to respond, remembering that the value 180°, will stay after the equal sign of the equation.
A)[tex]\sf x+125^{\circ}+80^{\circ}=180\\\\\\\sf x+205=180\\\\\\\sf x=180-205\\\\\\\boxed{\sf x=-25^{\circ}}[/tex]B)[tex]\sf x+68^{\circ}+318^{\circ}=180\\\\\\\sf x+386=180\\\\\\\sf x=180-386\\\\\\\boxed{\sf x=-206^{\circ}}[/tex]Okay?!Need help
She could also make yogurt at home for $1
$
1
a quart after spending $24
$
24
on a yogurt maker.
The graph shows the cost of yogurt bought at the grocery store and made at home.
Answers
The x-axis should be labeled quartz of yogurt.
The y-axis should be labeled total cost.
The slope of each line represents the cost of yogurt ($/qt).
The y-intercept of each line represents the initial equipment cost.
What is y-intercept?In Mathematics, the y-intercept is also known as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Based on the graph above, the initial equipment cost represents the y-intercept of each line.
What is a slope?In Mathematics, a slope is also referred to as gradient or rate of change and it is typically used to describe both the ratio, direction and steepness of the function of a straight line.
Therefore, the slope of each line represents the rate of change of the total cost with respect to the quartz of yogurt ($/qt).
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question:To make a certain shade of paint, Anya mixed 2/3 cups of white paint with 2 2/3 cups of blue paint
How many cups of blue paint should she mix with 3 cups of white paint to make the same shade?
Answers
Step-by-step explanation:
2/3 cups white paint mix with 2 2/3 cups = 8/3 cups blue paint.
so, 2/3 / 8/3 = 2×3 / 3×8 = 6/24 = 1/4.
therefore, the mix ratio white/blue paint is 1/4 (1 part white, 4 parts blue).
so, for 3 cups of white paint we need 3×4 = 12 cups of blue paint.
Write down the output y in terms of x
Input=x +2 x7 Output =y
Answers
Answer:
The answer is 14x
Step-by-step explanation:
2×7=14
x×14=14x
A store sells $2\frac{1}{4}$ pounds of mulch for every $1\frac{1}{2}$ pounds of gravel sold. The store sells $180$ pounds of mulch and gravel combined. How many pounds of each item does the store sell
Answers
Using the principle of proportional relationship, the amount of mulch and gravel sold is 108 and 72 pounds respectively.
Creating a ratio expression thus :
2.25 pounds of mulch = 1.5 pounds of gravel 2.25 : 1.5 Combined ratio= 2.25 + 1.5 = 3.75Let :
Pounds of mulch sold = mPounds of gravel sold = gPounds of Mulch sold :
(2.25/3.75) × 180 = 108 poundsPounds of gravel sold :
(1.5 / 3.75) × 180 = 72 poundsHence, the amount of mulch and gravel sold is 108 and 72 pounds respectively.
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The morning temperature in Finland was −18.3∘ F. The temperature rose 23.7°F during the day before reaching its high temperature for the day.
What was the high temperature for the day?
Enter your answer in the box.
°F
Answers
Answer:
The high temperature for the day was 5.4°F
Step-by-step explanation:
-18.3 + 23.7= 5.4
The high temperature for the day is 5.4° F.
What is temperature?Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.
Given that, The morning temperature in Finland was -18.3° F.
The temperature rose 23.7° F during the day before reaching its high temperature for the day.
Now, -18.3°+23.7°
= 5.4° F
Therefore, the high temperature for the day is 5.4° F.
Learn more about the temperature here:
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Whats the median, mode and range of 6, 8, 10, 10?
Answers
Answer:
Median: 9
Mode: 10
Range: 4
Step-by-step explanation:
Median
Line up all the numbers from smallest to biggest and take the one in the middle. In this case it's both 8 and 10. So you would do (8+10)/2. which is 9
Mode
it's the number that occurs the most number of times, which is 10.
Range
Range is 10-6, so it's 4.
A mean is an arithmetic average of a set of observations. The mean, median, and the range of the given data set 6, 8, 10, 10 are 8.5, 9, and 4 respectively.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The mean, median and range of the given data set 6, 8, 10, 10 is,
Mean = (6+8+10+10)/4 = 8.5Median = 9Range = 10-6 = 4Hence, the mean, median, and the range of the given data set 6, 8, 10, and 10 are 8.5, 9, and 4 respectively.
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One hundred students are assigned lockers 1 through 100. The students assigned to locker 1 opens all 100 lockers. The student assigned to locker 2 closes all lockers that are multiples of 2. The student assigned to locker 3 changes the status of all lockers ( e.g., locker 3 is open gets closed and locker 6 that is closed gets opened) The student assigned to locker 4 changed the status of all lockers whose multiples of 4, and so on for all 100 lockers.
PLEASE HELP ME I HAVEN'T STARTED ITS DUE TMRW
Answers
Answer:
The perfect square lockers are the only ones left open.
Step-by-step explanation:
Here is a legit link to an explanation of this old puzzle problem!
https://36university.com/act-math-locker-problem-solution/
Quoting from that page:
Method 2: Who Touches Which Lockers
Identifying which students touch which lockers is a little less of a brute-force approach and would likely have gotten you to the solution a little more quickly.
Here’s what I mean:
Consider locker #1. The only student who touches locker #1 is student #1. Student 1 opens the locker, and since no one else touches it, it will be left open at the end.
Consider locker #2. Student 1 opens the locker, and student 2 closes it. No one else touches the locker, so it will be closed.
Consider locker #10. Students 1 opens the locker. Student 2 closes it. Students 3 and 4 skip right by it. Student 5 opens it. Students 6, 7, 8, and 9 skip right by it. And student 10 closes it. Locker #10 will be closed.
Mental Milestone 1: After looking at several lockers, you should notice that lockers are only changed by student numbers that are factors of the locker number. In other words, locker 12 is changed by students 1, 2, 3, 4, 6, and 12.
Mental Milestone 2: You should also have noticed that factors always come in pairs. This means that for every student who opens a locker, there is another student who closes it. For locker #12, student 1 opens it, but student 12 closes it later. Student 2 opens it, but student 6 closes it later. Student 3 opens it, but student 4 closes it later.
By this logic, every locker would be closed.
But there are exceptions!
Consider locker #25. Student 1 opens it. Student 5 closes it. Student 25 opens it. The locker will be left open, but why? In this case, the factors do not come in pairs. One and 25 are a pair, but five times five is also 25. Five only counts as one factor. This causes the open-close pattern to be thrown off. Locker #25 is left open.
Mental Milestone 3: When factors don’t come in pairs, the locker will be left open. And factors don’t come in pairs when numbers are multiplied by themselves. Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100,…) are the only numbers whose factors don’t come in pairs because one set of factors, the square root, is multiplied by itself. This means that only perfect square lockers will be left open.
Locker #s 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are left open!
If you have a line with a Slope of -4 and a y-intercept of -2, what would be the equation of that line?
Question 6 options:
y = -4x + 2
y = -2x - 4
y = -4x - 2
y = -2x + 4
Answers
Answer:
y = -4x - 2
Step-by-step explanation:
y = mx + b where
m = slope, and b = y-intercept
slope = -4 = m
y-intercept = -2 = b
y = mx + b
y = -4x - 2
Answer: y = -4x - 2
The mean of 16, X, 3, 14,57 is 22. Find
Х
Answers
Answer:
20
Step-by-step explanation:
Given,
The mean of 16, X, 3, 14, 57 is 22.
Therefore,
(16+X+3+14+57)/5 = 22
(16+X+3+14+57) = 110
(90+X) = 110
X = 110-90
X = 20
The value of x will be 20.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mean of set 16, X, 3, 14, 57 is 22.
Now,
Since, The mean of 16, X, 3, 14, 57 is 22.
Hence, By definition of mean we get;
⇒ 16 + X + 3 + 14 + 57 / 5 = 22
Solve for x as;
⇒ 90 + X / 5 = 22
⇒ 90 + X = 22 × 5
⇒ 90 + X = 110
⇒ X = 110 - 90
⇒ X = 20
Thus, The value of x will be 20.
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Pleaaas help meeeee pleasssss
Answers
Answer:
For the first row, it's 6, 12, 18, 24, 30
Second row: 4, 8, 12, 16, 20
Step-by-step explanation:
You're just counting by multiples of 6 for the first row and 4 for the second row. Denominator means the number underneath the fraction line
ggraph this function
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Answer:
The graph of the equation x^2 - 4x - 5 is linked as a pdf down below.
Can someone double-check this to see if it's right?
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Answer:
yea it is
Step-by-step explanation:
If 11 - 3x = x, then 20x=
Answers
Answer:
20x = 55
Step-by-step explanation:
First you have to add 3x to both sides of 11-3x=x
[tex]11-3x=x\\+3x=+3x\\11=4x[/tex]
Now that you have 11 = 4x you divide 4 on both sides [tex]\frac{11}{4} =\frac{4x}{4}[/tex]
11/4 = x
But you can't divide 11 by 4 unless you are looking for the decimal form of 11/4 which is 2.75
so now we take 11/4 or 2.75 depending on if you need your answer in fraction or as a decimal and replace that with x however both will equal the number 55
[tex]20(\frac{11}{4})=55\\20(2.75)=55[/tex]
solve for x, find the measure of all angles plzzzzz!!
Answers
Answer:
∠ H = 22.5°, ∠ I = 45° , ∡ J = 112.5°
Step-by-step explanation:
The 3 angles in a triangle sum to 180° , then
x + 2x + 5x = 180 , that is
8x = 180 ( divide both sides by 8 )
x = 22.5
Then
∠ H = x = 22.5°
∠ I = 2x = 2 × 22.5° = 45°
∠ J = 5x = 5 × 22.5° = 112.5°