unit 5 relationships in triangles homework 1 triangle midsegments

Unit 5 Relationships In Triangles Homework 1 Triangle Midsegments

Answers

Answer 1

Based on the definition of a parallel line and the Midsegment Theorem the following are the right answers:

1. a.) BD║AE

b.) BF ║CE

c.) DF║CA

2. a.) YZ║RT

b.) RS ║XZ

c.) XY║TS

3. a.) FH = 24

b.) JL = 74

c.) KJ = 60

d.) FJ = 30

4. a.) AE = 26

b.) AN = 58

c.) CT = 21.5

d.) Perimeter of ΔAEN = 127

5. x = 15

6. x = 6

What are Parallel lines?

Parallel lines coplanar straight lines that do not meet each other and are equal distance from each other.

The Triangle Midsegment TheoremA midsegment is a line that connects the midpoints of the two sides of a triangle together. Every triangle three midsegments.Based on the Midsegment Theorem of a triangle, the third side of a triangle is always parallel to the midsegment, and thus, the third side is twice the size of the midsegment. In order words, length of midsegment = ½(length of third side).

Applying the definition of a parallel line and the Midsegment Theorem the following can be solved as shown below:

1. The pairs of parallel lines in ΔAEC (i.e. the midsegment is parallel to the third side) are:

a.) BD║AE

b.) BF ║CE

c.) DF║CA

2. The segment parallel to the given segments are:

a.) YZ║RT

b.) RS ║XZ

c.) XY║TS

3. Given:

FG = 37; KL = 48; GH = 30

a.) FH = ½(KL)

Substitute

FH = ½(48)

FH = 24

b.) JL = 2(FG)

Substitute

JL = 2(37)

JL = 74

c.) KJ = 2(GH)

Substitute

KJ = 2(30)

KJ = 60

d.) FJ = ½(KJ)

Substitute

FJ = ½(60)

FJ = 30

4. Given:

PT = 13

EN = 43

CP = 29

a.) AE = 2(PT)

Substitute

AE = 2(13)

AE = 26

b.) AN = 2(CP)

Substitute

AN = 2(29)

AN = 58

c.) CT = ½(EN)

Substitute

CT = ½(43)

CT = 21.5

d.) Perimeter of ΔAEN = EN + AN + AE

Substitute

Perimeter of ΔAEN = 43 + 58 + 26

Perimeter of ΔAEN = 127

5. 10x + 44 = 2(8x - 23) (midsegment theorem)

10x + 44 = 16x - 46

Add like terms together

10x - 16x = -44 - 46

-6x = -90

Divide both sides by -6

x = 15

6. 19x - 28 = 2(6x + 7) (midsegment theorem)

19x - 28 = 12x + 14

Add like terms together

19x - 12x = 28 + 14

7x = 42

Divide both sides by 7

x = 6

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Related Questions

What type of slope does the graph have!

Answers

Answer:

it either has a postive slope (when lines go uphill from left to right)

a negative slope (when lines go downhill from left to right)

a zero slope (when lines are horizontal)

or a undefined slope (when lines are vertical)

Step-by-step explanation:

hope this helps

Answer:

a negative slope of -2

Explanation:

slope = (y2-y1)/(x2-x1)

points (1,1) (0,3)

x1 = 0 y1 = 3

x2 = 1 y2 = 1

(1-3)/(1-0) = -2/1 = -2

Find the range for the measure of the third side of a triangle given the measures of two sides.
18 ft and 23 ft

Answers

The range for the measure of the third side of the triangle is (5, 38).

What is a triangle?

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

Two sides of the triangle are 18 ft and 23 ft.

Let the third side of the triangle is x cm.

Since, the third side is greater than the difference of the remaining sides and less than the sum of the two sides.

Implies that,

23 - 18 < x < 23 + 18

5 < x < 38

The range of the third side varies from (5, 38).

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Solve for X (x-4)(x-3)=0

Answers

[tex](x-4)(x-3) =0\\\\\implies x-4 = 0~~ \text{ or}~~ x - 3 = 0\\\\\implies x = 4~~ \text{or}~~ x = 3[/tex]

What is the circumference of a circle with a diameter of 14 feet?
A. 14 pi feet
B. 96pi feet
C 196pi feet
D. 7 pi feet

Answers

Solution-
Circumference of circle: 14 pi feet or 43.98.
But here answer is option A.
Answer:A
The answer is A. Hope this help

Please help trigonometry

Answers

Answer:

= 59.36

Step-by-step explanation:

S = 207

so, tan(16) = H/S

tan(16°) = 0.28674539

so H = tan(16) * S = 0.28674539 * 207 = 59.35629573

so the tree high = 59.36 foot

Solve for u. (u + 6)(u − 6) = 0

Answers

Answer:

u= 6, -6

Step-by-step explanation:

simplify the equation. Isolate the variable.

Hey there!

(u + 6)(u − 6) = 0

DISTRIBUTE “u” WITHIN the PARENTHESES

u(u) + (-6) + 6(u) + 6(-6) = 0

u^2 - 6u + 6u - 36 = 0

COMBINE the LIKE TERMS

u^2 - 36 = 0

ADD 36 to BOTH SIDES

u^2 - 36 + 36 = 0 + 36

CANCEL out: -36 + 36 because it gives you 0

KEEP: 0 + 36 because it helps solve for the u-value

NEW EQUATION: u^2 = 0 + 36

SIMPLIFY IT!

0 + 36 = 36

NEW EQUATION: u^2 = 36

TAKE the SQUARE ROOT

u = ± √36

u = -6 or u = 6

Therefore, your answer is: u = 6 or u = -6

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

please help brainliest if correct and best explanation

Answers

Answer: 120

Step-by-step explanation:

first you distribute 5 to 11 and -17 to get (55 - 85) then you distribute 6 to 14 and -7 to now get (55-85) + (84-42) then you distribute -12 to 2 and 7 to now have (55-85) + (84-42) - ( -24 + -84) to get 120 you multiple when you distruibute for these cause its outside the parenthesis so you multiply the number by everything in the parenthesis

Melody can cycle for 30 miles against the wind in the same amount of
time that is takes her to cycle 66 miles with the wind. If the speed of the
wind is 3 mph, what equation could be used to find Melody's speed
without any wind (x).

Answers

Answer:

15x/2*4

Step-by-step explanation:

Please help me.........

Answers

Answer:

8/15

Step-by-step explanation:

hope this helps!!! :D

Answer: 8/15

Step-by-step explanation: Tangent is opposite/adjacent

The hypotenuse, the longest side of a triangle which is 17. The adjacent side is the second longest which is 15. And the opposite is the shortest or the base of a triangle which is 8.

For the future, remember these:

Sin = opposite/hypotenuse

Cos = adjacent/hypotenuse

Tan = opposite/adjacent

Therefore, tan is 8/15.

Hope this helps.

Y'all... Please help I need help with freaking math...

Answers

15% of 850 is 127.5 and therefore the laptop would be reduced by 127.50

The sale price of the laptop is 722.50

PLEASE HELP WITH ALGEBRA WILL GIVE BRAINLIEST

Answers

Answer:

[tex]\frac{ad}{bd} + \frac{cb}{bd}[/tex]

Step-by-step explanation:

[tex]\frac{a}{b} + \frac{c}{d}[/tex]                          

[tex]\frac{ad}{bd} + \frac{cb}{bd}[/tex]                  Multiply  by the LCD (bd)

803 to 2:12
1,460 to 4:00
753 to 1:30
are these proportional?!?

Answers

Answer:

  no

Step-by-step explanation:

In terms of area per hour, Bob's works at the rate of ...

  1460 ft²/(4 h) = 365 ft²/h

Rhonda's rate is ...

  753 ft²/(1.5 h) = 502 ft²/h

The rates are different, so they are not proportional.

___

Additional comment

Toni's rate is 803 ft²/(2.2 h) = 365 ft²/h . . . the same as Bob's

Bob's and Toni's rates are proportional.

raplhy jogs at a rate of 4/2 miles in 2/5 of an hour. What is his speed in miles

Answers

Answer:

Ralph's speed is 2 miles in 24 minutes.

(Unit rate, Ralph runs 1 mile in 12 minutes)

Step-by-step explanation:

4 divided by 2 is 2 (miles)

2/5 of an hour is 24 minutes (60/5=12+12=24)

Please help me out

Fill in the blanks for this graph

1. This graph crosses the y-axis at______

2. The graph increases in the interval_____

3. The graph decreases in the interval____

Answers

Answer:

1 -5

don't know the answer of q2 and q3

Find the circumference of the object. Use 3.14 or 22 7 for ml. Diameter:9​

Answers

Answer:

c = 28.26 cm

Step-by-step explanation:

equation for circumference of a circle is 2πr

r = d/2 so here r = 9/2 = 4.5

2 x 3.14 x 4.5 = 28.26

Answer:

C ≈ 28.26 cm

Step-by-step explanation:

The circumference (C) is calculated as

C = πd ( d is the diameter ) , then

C = π × 9 ≈ 3.14 × 9 = 28.26 cm ( to the nearest hundredth )

Darren got 42 out of 56 correct on a test. What percent of the questions did he get correct?

Answers

Answer: Darren got 75% of the questions correct.

Step-by-step explanation:

To find the percentage of questions Darren got correct, we can divide the questions he got correct by the total number of questions.

42 ÷ 56 = 0.75

0.75 X 100 = 75

So, Darren got 75% of the questions correct.

what is the lowest common denominator for 2/3 and 3/5

Answers

the lowest common denominator is 15

Answer:

15

Step-by-step explanation:

3 times 5 is 15

Students majoring in engineering make up 21% of the students at a university. There are 6,600 total students enrolled at the university, How
many students are majoring in engineering?

Answers

Answer:

Step-by-step explanation:

21 percent of 6600 is 1386.

I'm sorry if I'm wrong.

please help me please

Answers

Answer:

x+2y = 5

2x+y=4

->

x+3y = 5

6x-y = 11

->

2x+y=10

x-3y=-2

Step-by-step explanation:

solutions of x and y for each system of equation can be solved by graphing

graph the two equations, and the intercepts of the two equations would be the x and y-values, aka the answers

if there are no intercepts, the equations have no solution

What is the slope of (-3, -2) and (-1, -5) ??

Answers

Answer:

-3/2 or -1 1/2

Step-by-step explanation:

The slope, plugging into the equation (y_2-y_1)/(x_2-x_1) would be -5 + 2 / -1 + 3, or -3/2, which can also be - 1 1/2

Answer:

-3/2

Step-by-step explanation:

slope ('m') formula:  (difference of the y-values) ÷ (difference of the x-values)

m = -2-(-5) ÷ -3-(-1)

m = 3 ÷ -2

slope = -3/2

For a new neighborhood, 100 acres of land will be split into 10 lots.​How many acres of land will each lot have?

Answers

10

Step-by-step explanation:

I think it's 10 my bad if I'm wrong

The thermostat for a house is set to 68 °F, but the actual temperature may vary
by as much as 2 °F. What is the range of possible temperatures?

Answers

Answer:

the range is 66 to 70 since it can be 2 degrees in either direction

The range of possible temperatures is 66 to 70°F.

It is required to find the range of possible temperatures.

What is Temperature?

The degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.

Given:

The thermostat for a house is set to 68 °F, but the actual temperature may vary by as much as 2 °F.

According to given question we have,

∴The range is 66 to 70 °F since it can be 2 degrees in either direction.

Therefore, the range of possible temperatures is 66 to 70°F.

Learn more about temperature here:

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ayy yo who want smok wit me

Answers

Meeeeeeeeeeeeeeeeeeee

Compare 37,007 and 30,707. Which
is greater?

Answers

Answer: 37,007 is greater

Step-by-step explanation:

Can i get a brainliest

Answer:

37,007 is greater than 30,707

Step-by-step explanation:

Thats because as you can see reading the numbers left to right, the first ones on the far left are both 3s. so so far they're the same. then go to the second number, making sure you're moving left to right. 7 is more than 0 therefor 37,007 is greater than 30,707

Question 4 of 10
Which statement about setting is true as it relates to a story?
A. Setting helps to define a story's point of view.
B. Setting is another word for characterization.
Ο Ο Ο
C. Setting affects character behavior, which drives the plot.
D. Setting comes into play at the end of a story.
SUBMIT

Answers

Answer:

First of all not a math question but wtv

the answer is C since where the story takes place affects what the characters do

Hope This Helps!!!

B setting is another word for characterization

Please help
What is the domain and range of the function

Answers

Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. They may also have been called the input and output of the function.)

Let w = 4. Enter >, <, or = to compare the expressions. 3w² + 1 10w + 8

Answers

Answer: ≥ without the line on the bottom.

Step-by-step explanation:

I am assuming the expression you are talking about are

[tex]3w^{2} +1[/tex] and [tex]10w+8[/tex].

If we were to replace w with 4 and calculate, we will find the answer:

[tex]3*4^{2} +1=3*16+1=48+1=49[/tex]

[tex]10*4+8=40+8=48[/tex]

Since the first expression, [tex]3w^{2} +1[/tex], is bigger than the second expression, the correct symbol to use is ≥ without the line on the bottom.

Which expression is equivalent to 7 − 9 ?

Answers

Answer:

Try subtracting 9 from 7 to find the value.

Step-by-step explanation:

Solve:
13/19- (-1/19)

Answers

It’s c I hope it works

Answer:

The answer is C! :) hope that helps haha

please help ill give brianliest to whoever gets the question right :)

Answers

Answer:

72

Step-by-step explanation:

I this problem I'm sure you're supposed to multiply: 24 x 3 = 72

hopefully this helped :)

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