Answer:
Statements Reasons
AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ Given
∠ADB and ∠CDB are right angles Given
ΔADB and ΔCDB are right triangles definition of right triangles
BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ reflexive property
ΔADB≅ΔCDB HL≅
AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ CPCTC (corresponding parts of congurent triangles must be congurent)
Step-by-step explanation:
Most of the geometry concepts and theorems that are learned in high school today were first discovered and proved by mathematicians such as Euclid thousands of years ago. Given that these geometry concepts and theorems have been known to be true for thousands of years, why is it important that you learn how to prove them for yourself?
Theorems and Proofs
In geometry, a postulate is a statement that is assumed to be true based on basic geometric principles. An example of a postulate is the statement “through any two points is exactly one line”. A long time ago, postulates were the ideas that were thought to be so obviously true they did not require a proof. A theorem is a mathematical statement that can and must be proven to be true. You've heard the word theorem before when you learned about the Pythagorean Theorem. Much of your future work in geometry will involve learning different theorems and proving they are true.
What does it mean to “prove” something? In the past you have often been asked to “justify your answer” or “explain your reasoning”. This is because it is important to be able to show your thinking to others so that ideally they can follow it and agree that you must be right. A proof is just a formal way of justifying your answer. In a proof your goal is to use given information and facts that everyone agrees are true to show that a new statement must also be true.
Suppose you are given the picture below and asked to prove that AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯. This means that you need to give a convincing mathematical argument as to why the line segments MUST be congruent.
Here is an example of a paragraph-style proof. This is similar to a detailed explanation you might have given in the past.
AB¯¯¯¯¯¯¯¯≅BC¯¯¯¯¯¯¯¯ because it is marked in the diagram. Also, ∠ADB and ∠CDB are both right angles because it is marked in the diagram. This means that △ADB and △CDB are right triangles because right triangles are triangles with right angles. Both triangles contain segment BD¯¯¯¯¯¯¯¯. BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ because of the reflexive property that any segment is congruent to itself. △ADB≅△CDB by HL≅ because they are right triangles with a pair of congruent legs and congruent hypotenuses. AD¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ because they are corresponding segments and corresponding parts of congruent triangles must be congruent.
There are two key components of any proof -- statements and reasons.
The statements are the claims that you are making throughout your proof that lead to what you are ultimately trying to prove is true. Statements are written in red throughout the previous proof.
The reasons are the reasons you give for why the statements must be true. Reasons are written in blue throughout the previous proof. If you don't give reasons, your proof is not convincing and so is not complete.
When writing a proof, your job is to make everything as clear as possible, because you need other people to be able to understand and believe your proof. Skipping steps and using complicated words is not helpful!
There are many different styles for writing proofs. In American high schools, a style of proof called the two-column proof has traditionally been the most common (see Example 3). In college and beyond, paragraph proofs are common. An example of a style of proof that is more visual is a flow diagram proof (see Example 4). No matter what style is used, the key components of statements and reasons must be present. You should be familiar with different styles of proof, but ultimately can use whichever style you prefer.
Learning to write proofs can be difficult. One of the best ways to learn is to study examples to get a sense for what proofs look like.
Answer:
False
Step-by-step explanation:
It doesn't need to be proven in order to be used. We can just assume the postulate is true.
Evaluate 8(a +b) when a = 5 and b = 11
Answer:
Hi there
your answer is 128
Step-by-step explanation:
8(5+11)
Answer:
128
Step-by-step explanation:
8(5+11)= 128
How much water do you add to make 75% sugar syrup using 99g sugar?
Answer: You will need 33ml of water added
Step-by-step explanation:
rs10,000 for 1 year at 8% per annum compounded half yearly.
Step-by-step explanation:
Answered 1 year, 9 months ago
Given,
Principal, P =Rs.10000, Rate, R = 8% per annum compounded half yearly for 1 year.
Now, There are two half years in a year. Therefore compounding has to be 2 times.
And rate = half of 10% = 5% half yearly.
Therefore, the required amount = = Rs. 10816
And Compound Interest, C.I. = Amount - Principal = Rs. (10816 - 10000) = Rs. 816.
hope it helps you
Last week, Jay had $217 in the bank, but this week, Jay is $28 in debt. Write an equation that describes that situation.
Answer:
?
Step-by-step explanation:
Answer:
217-245=-28
Step-by-step explanation:
Add $28 to $217, which is $245. Then subtract 245 from 217.
A pyramid has a rectangular base with edges of length 10 and 24. The vertex of the pyramid is directly 13 units above the center of the base. What is the: Total surface area of the pyramid?
Answer:
10 x 24 x 13 = 3120?
Step-by-step explanation:
I hope this is right!
Answer:
[tex]10\sqrt{313} +24\sqrt{194}+240[/tex] square units
Step-by-step explanation:
If your base is 10x24, and the vertical height is 13, you first have to find the slant height of the pyramid, in other words, calculate the hypotenuse of the triangles constructed using the height and the base divided by 2. You will need to find two slant heights as the base is not square. If you look at that image, the slant heights are marked in blue, and the specific measurements know are given in red. Using that, we can apply the Pythagorean theorem to determine the slant heights, which are [tex]\sqrt{194}[/tex] and [tex]\sqrt{313}[/tex], then we need to calculate the area of each triangular face. Thus they are [tex]5\sqrt{313}[/tex] and [tex]12\sqrt{194}[/tex], but there are two identical faces in the pyramid, which means we should double the area of the faces to achieve [tex]10\sqrt{313} +24\sqrt{194}[/tex], then we need to simply add the base as it's a face. So the answer is [tex]10\sqrt{313} +24\sqrt{194}+240[/tex]
Mr. Villa bought 91.25 inches of plastic
labeling tape. He will make labels 1.25 inches long
each. How many labels can he make?
1. What is asked in the problem?
A. the measurement of the tape
B. the labels can he make to the tape
C. inches of plastic labeling tape
D. Mr. Villas tape
2. What is the answer?
A. he can make 69 labels
B. he can make 70 labels
C. he can make 72 labels
D. he can make 73 labels
Answer:
1) B. the labels can he make to the tape
2) D. he can make 73 labels
Step-by-step explanation:
1) We are told that He will make labels 1.25 inches long each. We are asked the number of labels he can make.
Thus, correct answer is option B.
2) He wants to make labels 1.25 inches long out of 91.25 inches of plastic.
Thus, number of labels he can make = 91.25/1.25 = 73 labels
Help! I’ll mark brainly! I really need help don’t have much time ! Please help<3
write an expression for the perimeter of the triangle shown below 2.3x + 14 2x -0.2x + 15
Answer:
4.1x + 29
Step-by-step explanation:
So the perimeter would be the sum of all of the sides, so:
[tex]2.3x + 14 + 2x - 0.2x + 15\\= 4.1x + 29[/tex]
Answer: 4.5x+ 29 which is 3, so 3 is correct.
Step-by-step explanation:
P = a+b+c
First do the ordered pairs ( add the numbers with the x to the end, then add the other numbers with no x's)
1) Today's temperature will be at least 55°, but not more than 65º. Write and graph an inequality to show this situation.
Answer:
[tex]55 \leqslant x < 65 [/tex]
What is the equation for the line shown on this graph?
Christie has $3.80 in quarters and dimes. She has three more dimes than quarters. How many of each coin does she have?
Answer:
Quarters = 10
Dimes = 13
Step-by-step explanation:
Given that :
Quarters = $0.25
Dimes = $0.10
Total value =. $3.80
Let :
Quarters = a
Dimes = a + 3 (3 more dimes Than quarters)
0.25a + 0.10(a + 3) = 3.80
0.25a + 0.10a + 0.3 = 3.80
0.35a = 3.80 - 0.3
0.35a = 3.5
a = 3.5 / 0.35
a = 10
Quarters = a = 10
Dimes = a + 3 = 10 + 3 = 13
Find the measure of Angles A, C, D
Answer:
A= 65 C= 65 and D= 115
Step-by-step explanation:
given a parallelogram .
interior angles sum is 360 degree.
sum of adjacent angles is 180degree.
opposite angles are congruent (B=D).
A + B + C + D = 360
(A + D) + C + 115 = 360 since A and D are adjacent angles .
180 + 115 + C = 360
295 + C = 360
C = 360 - 295
C = 65
D = 115
A = 65
a+b+c+d=360
65 + 65 + 115 + 115 = 360
130 + 230 = 360
360 = 360
Can someone please help me!!! Ill mark brainliest!!
Answer: 252 ft
Find the area of the whole thing, then find the area of the green rectangle, then subtract to find the answer.
solve the inequality -3x + 6 > -2
Answer:
x<8/3
Step-by-step explanation:
Your answer is x is less than 8 over 3
Answer:
Answer is d
Step-by-step explanation:
x<8/
Solve 5x=45 using the opposite operation
Answer:
the answer is 8
Step-by-step explanation:
5 times 8 =45 5 time table
Answer:
9
Step-by-step explanation:
8x9=45
6.On Saturday, Jane likes to work out, eat, and read a book. She will either lift weights, run, or hike. Then she will choose 1 of the 6 restaurants near her home, and read either Harry Potter, Catcher in the Rye, or Girl on the Train. How many different ways can she spend her Saturday?
Answer:
Number of different ways can she spend her Saturday = 54
Step-by-step explanation:
Jane has to do three types of things - Work out , Eat and Read a book
In Work out -
She either lift weights, run, or hike
In Eating -
She will choose 1 of the 6 restaurants near her home
In Reading -
Read either Harry Potter, Catcher in the Rye, or Girl on the Train
Number of ways in which she can work put = ³C₁ = [tex]\frac{3!}{1! (3-1)!} = \frac{3!}{2!} = 3[/tex]
Number of ways in which she can eat = ⁶C₁ = [tex]\frac{6!}{1! (6-1)!} = \frac{6!}{5!} = 6[/tex]
Number of ways in which she can read = ³C₁ = [tex]\frac{3!}{1! (3-1)!} = \frac{3!}{2!} = 3[/tex]
So, Total number of ways = 3×6×3 = 54
Transform to slope-intercept form. 1+2y=6x-3
Answer: Y=3X-2
Step-by-step explanation:
First you are gonna need to combine all like factors.
1+2y=6x-3 (subtract 1 from both sides)
2y=6x-4
Then you need to get the y by itself.
2y=6x-4 (divide all terms by 2)
y=3x-2
now you are in slope intercept form (y=mx+b)
Put the numbers in order from smallest to largest
-10,-1,0,10,1
Answer:
The order is (-10,-1,0,1,10)
Answer:
-10 -1 0 1 10
Step-by-step explanation:
as -10 is smaller than -1 is because the negative numbers keep getting smaller as they progress for example 1 and 10 which is bigger it is ofc 10 but I negative numbers its quite the opposite hope this helps
A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours.
A. True
O
B. False
A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.
What is Speed?Speed is the time rate at which an object is moving along a path,
Given that car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours.
We have to check whether the statement is true or false.
To check, we can use the formula:
distance = rate x time
Substituting the given values, we get:
distance = 60 x 4.5 = 270 miles
Therefore, the statement is true.
Hence, A car traveling at an average rate of 60 miles per hour will drive 270 miles in 4.5 hours is true.
To learn more on Speed click:
https://brainly.com/question/28224010
#SPJ2
Please I need this TOMORROW
Answer:
here u go !! <3
Part 1:
1. 18 - [(15 - 9 + 4] - 2 = 6
2. 6² - [3² + (3 + 12)] = 12
3. 21 - [(2 × 4) + 2 + 5] = 6
4. [(17 - 10) + 4] + 5² = 36
5. 36 ÷ 6 + [(5 × 3) + (13 - 6) + 10] = 38
Part 2:
6. 15 ÷ 3 × 5 - 16 = c. 9
7. 2 [5 + (30 ÷ 6)²] = d. 60
8. [3² × 4] - [6 + 4²] = b. 14
9. 8 [6² - 3 × (2 + 5) - 8 + 3] = e. 80
10. 15 - {27 - 2 × [33 - 4 × (5 + 1)]} = a. 6
Answer:
(1 )14
(2) 45
(3) 20
(4) 36
(5)121
(6) 6
(7)9
(8) 14
(9)80
(10)60
PLEASE HELP! I WILL GIVE BRAINLIEST!!
One side of a rectangle is 9 inches longer than another side. If the longer sides of this rectangle decreases by 5 inches and the shorter sides increases by 3 inches, the area of the new rectangle equals the area of the original rectangle. Find the dimensions of the original rectangle
Answer: The original rectangle was 15 inches by 6 inches
=============================================================
Explanation:
L = original lengthW = original widthLet's make the length longer than the width, so L = W+9 since we're told that one side is 9 inches longer than another.
The area of this rectangle is
Area = length*width
A = L*W
Through substitution, we can replace L with W+9
A = (W+9)W
A = W^2 + 9W
We'll come back to this later.
--------------
Now let's decrease the longer side L by 5 inches to get L-5. At the same time, we'll increase the shorter side W by 3 to get W+3.
The new rectangle is (L-5) inches by (W+3) inches which leads to the area of...
A = (length)*(width)
A = (L-5)*(W+3)
A = (W+9-5)*(W+3) .... L replaced with W+9
A = (W+4)(W+3)
A = W^2 + 3W + 4W + 12 .... FOIL rule
A = W^2 + 7W + 12
--------------
We found these two area expressions
W^2 + 9WW^2 + 7W + 12We're told that the two areas (of the original and new rectangle) are equal to one another. Set them equal to each other and solve for W
W^2 + 9W = W^2 + 7W + 12
9W = 7W + 12 ............ subtracted W^2 from both sides
9W-7W = 12
2W = 12
W = 12/2
W = 6
The original width is 6 inches
L = W+9 = 6+9 = 15
The original length is 15 inches
The original area is L*W = 15*6 = 90 square inches
The new rectangle has side lengths of (L-5) = (15-5) = 10 inches and (W+3) = (6+3) = 9 inches. Then note how the area of this new rectangle is 10*9 = 90 square inches to match the other area. This helps confirm we have the correct answer.
Answer:
15 by 6
sorry i dont know how to do it
How do I solve this??? LOL
Answer: y=8
Step-by-step explanation: 4y-4+3y=52
Alfredo's bank charges an $8 service fee each month if his account goes below $500. In June, Alfredo had $510 in his account. He withdrew $25 and then did not have any transactions in his account for 6 months. a. Write as an integer the amount by which Alfredo's bank balance changed during the six months.
Answer:
$48
Step-by-step explanation:
Given that he is charged $8 service fee each month if his account goes below $500. If he has $510 and withdraws $25 the amount in account would be
= $510 - $25
= $485
This is below $500 hence he will be charged $8
Since he did not have any transactions in his account for 6 months, the change in his account as a result of the monthly charge
= 6 * $8
= $48
witch of the following statements is true
Answer:
in pretty sure its bfg is a right angle
Answer:
second one
Step-by-step explanation:
have a great day
Solve this equation:
-5(x - 2) - 3x = -80
Answer:
x=45/4
Decimal Form:
x=11.25
Mixed Number Form:
x=11 1/4
Step-by-step explanation: PLEASE MARK ME BRANLIST AND IF U CAN ANSWER MY QUESTION FROM MY PROFIL WOULD BE NICE.
HAVE A GREAT DAY! ❤️
At a restaurant, the cost for one breakfast taco and one glass of milk is $2.10. The cost for two tacos and three glasses of milk is $5.15.
Write a system of equations to represent this situation. DO NOT SOLVE.
Let x = # of tacos and y = # of glasses of milk.
Answer:
2x+3y=5.15
Step-by-step explanation:
10 POINTS FOR WHOEVER ANWSERS!
Answer:
Infinitely many solutions
Step-by-step explanation:
what is the answer to 2 (r-4)+5(r+2
Answer:
7r + 2
Step-by-step explanation:
I hope this helps have a great day
AI need help with this math homework ASAP I need the independent variable the dependent and the equation
Answer:
b is the independent variable
c is the dependent variable
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is the least common multiple of 8, 7, and 2?
Answer:
1 i know its one hope it help
Step-by-step explanation:
List all prime factors for each number.
Prime Factorization of 2 shows:
2 is prime => 21
Prime Factorization of 7 shows:
7 is prime => 71
Prime Factorization of 8 is:
2 x 2 x 2 => 23
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 7
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 7 = 56
In exponential form:
LCM = 2^3 x 7^1 = 56
LCM = 56
Therefore,
LCM(2, 7, 8) = 56
