Given: y || z
Prove: mZ5+ m2 2 + m26 = 180°
Angles Lines Statements Reasons
21
23
25
26
m21
m23
m25
m26
L
A
M
1
2
3
y
Statements
Reasons
4
5
6
7
z
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Intro
D
Answers
Using the above statements and reasons can be used to prove the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
What is the Triangle Sum Theorem?The triangle sum theorem states that, when we add the all three interior angles of a triangle together, it will give us a sum of 180°.
Given that y || z:
∠1 ≅ ∠5 and ∠3 ≅ ∠6 based on the interior angles theorem. This implies that:
∠1 = ∠5 and ∠3 = ∠6 (Eqn. 1)
m∠LAM = 180° (def. of straight line angle)
Thus, using the angles addition theorem, we have:
∠1 + ∠2 + ∠3 = m∠LAM
∠1 + ∠2 + ∠3 = 180° (eqn. 2).
Using eqn. 1 and eqn. 2, substitute ∠1 = ∠5 and ∠3 = ∠6 into eqn. 2.
∠5 + ∠2 + ∠6 = 180° (substitution).
Therefore, using the above statements and reasons can be used to prove the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
Learn more about triangle sum theorem on:
https://brainly.com/question/7696843
The proof for the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
What is Angle Sum Property?According to the triangle sum theorem, if we total up a triangle's three internal angles, we receive a value of 180°.
We have, y || z.
So, ∠1 ≅ ∠5 and ∠3 ≅ ∠6 (Alternate Interior Angle)
Using Linear Pair
∠1 + ∠2 + ∠3 = m ∠LAM
∠1 + ∠2 + ∠3 = 180°
Now, substitute ∠1 = ∠5 and ∠3 = ∠6 in above equation
∠5 + ∠2 + ∠6 = 180° .
Thus, using the above statements can be used to prove the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
Learn more about Angle Sum Property here:
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Related Questions
Solve the inequality 2(4x – 3) ≤ 5x – 27
Answers
Answer:
( -7, ∞)
Step-by-step explanation:
2(4x - 3) ≥ 5x - 27
8x - 6 ≥ 5x - 27
3x - 6 ≥ -27
3x ≥ -27 +6
3x ≥ -21
x ≥ -7
All numbers great than -7
Which expression is equivalent to -14x + 28?
Answers
Answer:
B. 2x-3
Step-by-step explanation:
14 and 21 have a common factor which is 7 so divide both by 7 to get 2x-3.
(-5,1) and (-5,4) what is the slope of the line that passes through the given points
Answers
Answer:
Undefined
Step-by-step explanation:
I always like to take a good look at the points before I go about solving for the line. To me, it looks like this is going to be a vertical line. Why do I think that? Well, for each point, the x-value is -5. Since this is a linear function, every other point must also have an x-value of -5. So, our line would be straight up and down, going through the x-intercept (-5, 0). Let's try out this theory by subtracting our y-values and then our x-values, then dividing:
[tex]\frac{4-1}{-5-(-5)} =\frac{3}{-5+5} =\frac{3}{0}[/tex]
And that makes sense! Functions that show up as vertical lines are undefined, since their slopes always have 0 as a denominator, and anything divided by 0 turns out to be undefined. So, that's our answer - the slope is undefined.
Hopefully that's helpful! :)
Answer:
undefined
Step-by-step explanation:
(-5, 1) and (-5, 4) lie on the same vertical line.
A vertical line has undefined slope.
Find the cosine of angle U
Answers
Answer:
1st option
Step-by-step explanation:
cosU = [tex]\frac{asjacent}{hypotenuse}[/tex] = [tex]\frac{UV}{UW}[/tex] = [tex]\frac{15}{17}[/tex]
There are 495 pages in the mathematic book, from this 330 pages are included for the first term. Find the proportion of total pages to allotted pages in simplest form.
Answers
Answer:
330/495 = 2/3
the answer is 2/3
Answer:
3 : 2
Step-by-step explanation:
Total pages : allotted pages = 495 : 330
Find the HCF of 495 and 330
495 = 5 * 3*3*11
330 = 5 * 3 * 2 * 11
HCF = 5 * 3 * 11 = 165
Divide 495 and 330 by 165
495 : 330 = 3 : 2
dose anyone know the answers?
Answers
Answer:
Number 1 is 3.5, Number 2 is 4.29(because their are 30 days in april), Number 3 is 11, Number 4 is 90.5 miles per hour(MPH) i think
Step-by-step explanation:
I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT
Answers
Answer:
115°
Step-by-step explanation:
From E to B is 180°.
So when looking at angle ACB we get 65°
The angle ACE is equal to 180° - °65 = 115°
To show this is correct we have to add ACE and ACB and that should equal 180° which is true.
Answer:
115°
Step-by-step explanation:
normally straight lines are 180°
so angle ACF is already 90°
to find E, we need to subtract the 90°and the 65°
here it is: 180-(90+ 65)
= 25°
so finally ACE = 90° + 25°
= 115°
;)
The sum of two consecutive even integers is 122. What are the two numbers?
Answers
Answer:
Let the first number = xTherefore, the other number = x + 2 (x+2 is so as in two consecutive even numbers there is 1 odd number) Now, According to questionx + x + 2 = 1222x + 2 = 1222x = 122-22x = 120x = 120/2x = 60Now, first no. = x = 60Therefore, second no. = x + 2 = 60 + 2 = 62Equation 60 + 62 = 122Step-by-step explanation:
If you like my answer than please mark me brainliest
Answer:
The numbers are : 60 , 62
Step-by-step explanation:
Let the two consecutive even numbers be 2x , 2x + 2
2x + 2x + 2 = 122
Combine like terms
4x + 2 = 122
Subtract 2 from both sides
4x = 122 - 2
4x = 120
x = 120/4
x = 30
2x = 2*30 = 60
2x + 2 = 2*30 + 2 = 60 + 2 = 62
try these.Evaluate the following logarithms.
Answers
Answer:
Reminder: [tex]log _a x[/tex] answers the question: "what power do I have to raise a to in order to get x?"
Thus said.
[tex]1. \ 64= 2^6 = 4^3 \implies log_464=3\\2. \ 5^1 = 5 \implies log_55 = 1\\3.\ 3^1=3; \ 2^1=2 \implies Log_33 + log_22 = 1+1=2\\4.\ 5^1=5; \ 8^1=8 \implies log_55 - log_88=1-1=0\\5. \ 8=2^3; 32=2^5 \implies log_28+log_232 = 3+5=8[/tex]
Last one, if you already talked about log properties, can be handled as:
[tex]log_28+log_232= log_2(8\times32) = log_2256 =8\ (256=2^8)[/tex]
Find the value of x in the triangle shown below.
102
48
Answers
Answer:
The sum of the angles of a triangle is always 180, so the answer is
180-102-48=30
Step-by-step explanation:
7. Write an inequality that matches the graph shown.
Answers
Answer:
To make an inequality its in the part that is shaded so
Step-by-step explanation:
(-2,-2) (-4,1) ETC
Simplyfy (4^7/5^2)^3
Answers
Find a point-slope form for the line with slope
and passing through the point (-4,-7).
Answers
Answer:
[tex]\displaystyle y + 7 = \frac{1}{5}(x + 4)[/tex]
General Formulas and Concepts:
Algebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeStep-by-step explanation:
Step 1: Define
Identify variables.
Point (-4, -7)
Slope m = [tex]\displaystyle \frac{1}{5}[/tex]
Step 2: Find Equation
Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - -7 = \frac{1}{5}(x - -4)[/tex]Simplify: [tex]\displaystyle y + 7 = \frac{1}{5}(x + 4)[/tex]HELP MEEEEEEEE PLEASE
Answers
Answer:
Option A (3/4)
Step-by-step explanation:
Please mark Brainliest
Answer:
THATS CORREC T
Step-by-step explanation:
CAUSE A IS THE RIGHT ONE THE REST BIS WRONG BUT IT CAN E CONFUSING
Nicole is running for school president. Her best friend designed her campaign poster, which measured 3 feet by 2 feet. Nicole liked her poster so much, she reproduced the artwork on rectangular buttons that measured 2 inches by 1 1/3 inches. What is the scale factor?
Answers
Answer:
1 feet = 12 inches3 feet = 36 inchesLarger of buttons dimension is 2 inches
Step-by-step explanation:
To make 100g of jam you need 57g of strawberries, 17g of blackberries and the rest should be sugar.
What is the ratio of blackberries to sugar?
Give your answer in its simplest form.
Answers
2. Now, we can write the ratio of blackberries to sugar as 17:26. This can’t be simplified
Answer = 17:26
Hope this helps
ggraph this function
Answers
Answer:
The graph of the equation x^2 - 4x - 5 is linked as a pdf down below.
What is mZ2 + m 3? А 1 2 3 4 D m22 + m 23 =
Answers
Answer:
link
Step-by-step explanation:
F = 1/5 gh^2
solve for h
Answers
Answer:
First of all, let's multiply both sides by 5, clearing the denominators:
Then, as long as g is not zero, we can divide by g, and let's read right to left:
At this point, assuming F and g are either both positive or both negative, we can take the square root of both sides:
If h represent a quantity that is positive by it's nature (ie, the length of a segment) you can consider only the positive root, ie ignoring the plus or minus sign.
SnackTime Foods produced 3,181,990 grams of popcorn last year, which was placed in 7- gram bags. How many bags did the company fill? bags Submit
Answers
Answer:
The company filled 454570 bags.
Step-by-step explanation:
Rick buys 3 CDs and 5 video games. The cost of one video game is $12.00 more than the cost of one CD. If Rick spends $164.00, what is the cost of each CD?
Answers
Step-by-step explanation:
x = price per video game
y = price per CD
164 = 5x + 3y
and then we know
x = y + 12
now we can use this as substitute in the first equation :
164 = 5(y + 12) + 3y = 5y + 60 + 3y = 8y + 60
104 = 8y
y = $13
x = y + 12 = 13 + 12 = $25
so, each CD costs $13.
Which one is not a function? And why not ?
Answers
Answer:
the selected answer/2
Step-by-step explanation:
not a function because the same y has 2 different x values
HELP PLEASE!!!
Identify a point and two x intercepts to write the x-intercept form equation of each parabola.
Answers
x intercepts are 5 and 7
The third point I used was (6,-2); however, you can use any other point you want as long as it's not one of the x intercepts mentioned.
==========================================================
Explanation:
The x intercepts are 5 and 7, where the parabola crosses the x axis. Because of these roots, the two factors are x-5 and x-7.
We can think of the root x = 5 turning into x-5 = 0 after subtracting 5 from both sides. The same goes for x = 7 turning into x-7 = 0.
Put together, the two factors lead to (x-5)(x-7) and we get the equation y = (x-5)(x-7). Plugging either x = 5 or x = 7 into this equation produces y = 0.
-------------------
Notice that plugging in x = 6 leads to...
y = (x-5)(x-7)
y = (6-5)(6-7)
y = (1)(-1)
y = -1
However, the graph shows that x = 6 should lead to y = -2 instead. To fix this, we can stick a 2 out front like so
y = 2(x-5)(x-7)
y = 2(6-5)(6-7)
y = 2(1)(-1)
y = -2
The error has been fixed. As you can see, we need this third point to help nail down the parabolic equation. You can pick any other x value you want as long as it's not 5 or 7.
-------------------
Let's try another x value. Let's say we pick x = 8
y = 2(x-5)(x-7)
y = 2(8-5)(8-7)
y = 2(3)(1)
y = 6
We see that x = 8 leads to y = 6. This matches what the graph shows that (8,6) is a point on the parabola. I'll let you try other x values.
-------------------
In short, we used the roots 5 and 7 to generate the partial factorization (x-5)(x-7). Then we used a third point (6,-2) to help determine the coefficient out front which was 2.
So after using that point, we go from y = (x-5)(x-7) to y = 2(x-5)(x-7) which is the final answer. This is considered x-intercept form because we can quickly read off the x intercepts from this equation.
It is normal for some newborn babies to lose weight in their first week of life. Baby Todd's birth weight was 10 pounds. One week after being born, he is 10% lighter. What is Todd's current weight? pounds
Answers
Answer:
9 pounds
Step-by-step explanation:
you can use cross multiplication to find 10percent of 10 pounds, then subtract this from 10 pounds
A rhombus is a special parallelogram. Which are true about a rhombus that is not true about all parallelograms? Pick up to 3 answers. A. Diagonals create a right angle where they interesect B. All sides are congruent C. Diagonals bisect vertex angles D. Diagonals are congruent E. Opposite angles are congruent
Answers
The statement that is true about a rhombus that is not true about all parallelograms are as follows;
Diagonals create a right angle where they intersect All sides are congruent Diagonals bisect vertex anglesDiagonals of a rhombus are perpendicular bisector of each other. This means they form a right angle where they intersect.
This is not true for parallelograms. The diagonal only bisects each other.
All sides are congruent for a rhombus .
This is not true for a parallelogram. Only opposite sides are congruent for a parallelogram.
The diagonal bisect the vertex angles of the rhombus.
This is not true for a parallelogram.
read more: https://brainly.com/question/4165249?referrer=searchResults
PLZZZ HELP ASAP I NEED IT FAST!
Answers
Answer:
5.4
Step-by-step explanation:
Step 1: Take any two side lengths from the quadrilaterals (one from ABCD and one from PQRS)
For this case, I'm going to take 4 and 7.2Step 2: Divide the length you took from PQRS by the length you took from ABCD.
[tex]\frac{7.2}{4}[/tex] [tex]1.8[/tex] (1.8 is the scale factor (SF))Step 3: Since CD and RS and corresponding sides, multiply 3 by 1.8
[tex]3 * 1.8[/tex] [tex]5.4[/tex]Therefore, x = 5.4.
Answer:
5.4
Step-by-step explanation:
Look at photo for explanation
What is the answer to this question?
Answers
Answer:
Perimiter would be 30cm
Step-by-step explanation:
3+3+6+3+6+3+6
Help please no funny stuff!
The last one is
10,15
20,25
8,30
20,35
Answers
Answer:
the last one none over lap
What is the slope of the line that passes through the ordered pairs(1,14)and(−5,−34)?
Answers
Answer:
The answer is 8!
Step-by-step explanation:
I took the quiz. Have a great day, hope this helps!
If I have 4 magazines, and each magazines has 13 bullets, And there are 30 people in class and you need 4 bullets for each person. How many people get 4 bullets.
Answers
Answer:
13Step-by-step explanation:
4 magazines, and each magazines has 13 bullets:
4*13 = 52 bullets4 bullets for each person:
52/4 = 13 people