Given: BE and AD are altitudes (intersecting at H) of triangle ABC, while F,G, and K are midpoints of AH, AB and BC, respectively. Prove: angle FGK is a right angle.

Answers

Answer 1

Solution :

Since [tex]BE[/tex] is an altitude of a triangle [tex]ABC[/tex], it is perpendicular to [tex]AC[/tex] (since the triangle ).

Since [tex]G[/tex] and [tex]K[/tex] are the midpoints, then the line [tex]BG=GA[/tex] and the line [tex]BK=KC[/tex]. The line [tex]KG[/tex] must be parallel to the line [tex]AC[/tex] and is therefore perpendicular to [tex]BE.[/tex]

Now since F and [tex]G[/tex] are the mid points, we get [tex]GA=BG[/tex]. The line [tex]GF[/tex] is parallel to BH and is perpendicular to AC.

Therefore, we have

[tex]KG-GK[/tex] parallel to [tex]AC[/tex]

[tex]AC[/tex] perpendicular to [tex]BE-BH-BJ[/tex]

[tex]BE-BH-BJ[/tex] parallel to [tex]GF[/tex]

Thus [tex]GK[/tex] is perpendicular to [tex]GF[/tex] and also ∠[tex]FGK[/tex] is a right angle.

Given: BE And AD Are Altitudes (intersecting At H) Of Triangle ABC, While F,G, And K Are Midpoints Of

Related Questions

(40 POINTS) Which linear function represents this table of values?

A. y=16x+13
B. y=23x+7
C. y=32x−3
D. y=6x−9

x: y:
3 9
9 13
12 15

Answers

Answer:

B is the answer

Step-by-step explanation:

take two of the points to plug in and test

point one, when x is 3 y is 9

y=2/3 (3) +7

y=6/3 +7

y= 2 + 7

y=9

test the next point

(9,13)

y=2/3 (9) + 7

y=18/3 +7

y= 6 +7

y=13

It is given that 2(3+x)=6+2x this is e so ample of which property

Answers

Answer:

distributive property

Step-by-step explanation:

The distributive property is the one that says a multiplier outside parentheses is equivalent to multiplication of every term inside parentheses.

2(3 +x) = 2(3) +2(x) = 6 +2x

Decimal Addition/Subtraction.

Answers

Answer:

D. 1.175L

Step-by-step explanation:

NEED HELP ASAP WILL GIVE BRAINLIESTfor which values of x does each expression make sense?sqrt x+5

Answers

Answer:

can I see a picture? so I can try & help u

Answer:

x≥-5

Step-by-step explanation:

what does it mean when the will says tomorrow it's ashes will be scattered to the four winds in the westing game

Answers

Answer:

In the document, Westing names the sixteen heirs present as his “nieces and nephews” and says that tomorrow his ashes “will be scattered to the four winds.” He then asserts that his life has been taken by one of his heirs, and he promises that the heir who finds something will receive the inheritance

Step-by-step explanation:

Westing names the sixteen heirs present as his “nieces and nephews” and says that tomorrow his ashes “will be scattered to the four winds.” He then asserts that his life has been taken by one of his heirs, and he promises that the heir who finds something will receive the inheritance.

What are the main events in The Westing Game?

The main events in the Westing Game include moving into Sunset Towers, the Halloween dare, the reading of Samuel Westing's will, and the pairing of teams. Finally, the solving of clues and ultimately solving the puzzle.

Who Wins The Westing Game?

Several years after that, Turtle stays with Sandy/Westing (as Eastman) while he really dies. She finally wins the prize and goes to play chess with her niece Alice.

Learn more about the Westing Game here: brainly.com/question/16545687

#SPJ2

The Truth Table Represents Statement P,Q,R

Which statement is true for rows A, C and E

R—> (p^q)
R—>(p v q)
(q^r)—>p
(q v r) —>p

Answers

Recall that a ⇒ b ≡ ¬a ∨ b.

• r ⇒ (p ∧ q) ≡ ¬r ∨ (p ∧ q)

In row C, q is false so p ∧ q false, and r is true so ¬r is false.

¬r ∨ (p ∧ q) ≡ false ∨ false ≡ false

• r ⇒ (p ∨ q) ≡ ¬r ∨ (p ∨ q) = p ∨ q ∨ ¬r

In each of rows A, C, and E, at least one of p or q is true, so

p ∨ q ∨ ¬r = true

• (q ∧ r) ⇒ p ≡ ¬(q ∧ r) ∨ p ≡ (¬q ∨ ¬ r) ∨ p = p ∨ ¬q ∨ ¬r

In row E, p is false and both q and r are true, so ¬q and ¬r are both false.

false ∨ false ∨ false = false

• (q ∨ r) ⇒ p ≡ ¬(q ∨ r) ∨ p ≡ (¬q ∧ ¬r) ∨ p

In row E, p is false and both q and r are true, so both ¬q and ¬r are false.

(¬q ∧ ¬r) ∨ p ≡ (false ∧ false) ∨ false ≡ false ∨ false ≡ false

If N = 6 x 2 x 3, what is the value of N?

Answers

Answer:N= 36

Step-by-step explanation:

Which has a greater rate of change?
pick one

Answers

I think the yellow line.
It’s the steepest so I has the greatest rate of change.

slopeeeeeeeeeee please help me someone no bots

Answers

Answer:

5) -2

6) 1

7) -4/3

8) I'm not sure for this one

9) 8

10) 9/5 i think

1) A

2) D or A

3) C

4) A

Step-by-step explanation:

Slope intercept form: y = mx + b, and m is the slope, and b is the y-intercept

Help for brainliest plz

Answers

Answer:

oh uhm that is 3,4 <3

Step-by-step explanation:

It will be 3,4 that will be your answer

you got this
{2x−y=3
x+2y=−6

Answers

Answer:

Equation form

x=0

y=-3

Point form

(0,-3)

Step-by-step explanation:

simplify expression

3+2+y+y

Answers

Answer:

2y + 5

Step-by-step explanation:

I hope this helps!

Hey there!

3 + 2 + y + y

= 3 + 2 + 1y + 1y

COMBINE the LIKE TERMS

= (3 + 2) + (1y + 1y)

= 5 + 2y

= 2y + 5

Therefore, your answer is: 2y + 5

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

please help me and NOOO LINKS

Answers

Answer:

whats the shape

Step-by-step explanation:

HELP WITH MATH!! MARKUPS AND MARKDOWNS! I’LL PUT BRAINLIEST IF ITS CORRECT!

Answers

Answer:

1. $62.50

2. $41.25

3. $90.35

4. $2,160

5. $343

6. $66,602.25

7. $220

Step-by-step explanation:

g(x) = 3x + 1; Find g(7)

Answers

g(7)=3(7)+1
g(7)=21+1
g(7)=22

Given that D(x) = 2x, select all of the following that are true statements.
D( x) is a direct variation.
O D( x) is a function.
D( X) is a rule for the set of points (5, 10), (6, 12) and (-2,-4).
O xls the dependent variable.
D(6) = 3

Answers

It is D
You welcome

please help ASAP!!!

Answers

Answer: y = 115 and x = 78

Step-by-step explanation:

y = 115 because it is parallel with the angle 115 and parallel are congruent, for x find the angle beside the angle 102 and that angle is parallel with the angle x and that will be 180 - 102 = 78 which is x

In mosquito, more itchy bites are dominate to less itchy bites. If a male mosquito with a heterogeneous, more itchy bite mates with a less itchy, homologous female, what will the offspring likely be like?

4 Points Total:

Key (assign letters and traits) 1

Correct Punnet square 1

Correct phenotype 1

Correct prototypes 1

Answers

Answer:

a rash

Step-by-step explanation:

What is the length of
BC
X + 9
2x - 8
Enter your answer in the box.
units
х
B
1

Answers

Answer:

17 units

Step-by-step explanation:

Because the triangle is isosceles, 2 of its sides are congruent; namely, the two sides that are opposite of the 2 congruent angles are contruent.

Because of the reason stated above, we can see that AC is congruent to BC, meaning that:

x+9=2x-8

-x -x

9=x-8

+8 +8

17 = x

Notice that BC is equal to x, so 17 is our final answer.

Solve this please do the model

Answers

First solve by converting the mixed fraction into an improper fraction. Multiply 3 by 4 and add it to 3 and put it over 4 to get 15/4. Now multiply 2 by the numerator to get 30/4. Not convert to mixed fraction and you get 7 and 1/2 as an area.

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Answers

Answer:the answer is 22/9 or in mixed form would be 2 4/9 but in decimal it’s 2.4 but the 4 is repeated

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Answers

It’s c I hope it works

Answer:

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How many ways are possible to select a president and vice president from an
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Answers

The Answer there are 9*8 = 72 ways to choose a president and vice president

Step-by-step explanation:

Solve the following inequality.
20 < 8

Answers

Answer:

x > 12/7

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Step-by-step explanation:

7x + 8 > 20

Subtract 8 from each side

7x+8-8 > 20-8

7x > 12

Divide each side by 7

7x/7 > 12/7

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Answers

Answer:

hehehehehehe

Step-by-step explanation:

ssa

Can someone please help me with this and tell me the points?

Answers

Answer:

Graph: Refer to attached image

Solution: (-5,-3)

Step-by-step explanation:

First graph to two equations.

Refer to the image attached to see what the equations would look like when graphed.

Wherever they intersect is the solution.

They intersect at (-5,-3) therefore (-5,-3) is the solution to the system of equations

in a supermarket, bottles of lemonade are on a buy one get one half price offer.
The normal price of lemonade is 82p.
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£

Answers

Answer: 114p

Step-by-step explanation:

Hope it helps

To make I a subject of the formula V = IR, we *
subtract R from both sides
multiply both sides by R
divide both sides by R
divide both sides by I

Answers

The original

Equation is V = IR

Where I is multiplied by R

To solve for I you need to isolate it by dividing both sides by R

I = V/ R

Answer: divide both sides by R

Answer:

To make I a subject of the formula V = IR, we divide both sides by R.

Step-by-step explanation:

V = IR

V/R =IR/R

The R in IR/R cancels out because it is on the other side.

We then have:

V/R = I

Which can be written as:

I = V/R

Hope this helps! Have a great day!

Starfish have about 15,000 tiny feet that help them move around the ocean floor. The table shows the distance traveled by a starfish over a given time.

Answers

Answer: its ''A'' it takes a starfish 60 seconds to travel 1 meter

Step-by-step explanation:

Answer:

Step-by-step explanation:

6. The Gonzales family has three children. On summer break, they went to an amusement park. They bought 3 child tickets for $18.50 and 2 adult tickets. If they spent a total of $104.50, how much was the price of each adult ticket? and what is the equation.

Answers

Answer:

$24.50

Step-by-step explanation:

18.50*3=55.50 dollars

104.50-55.50=49.00 dollars

49 divided by 2=24.50 dollars

$24.50 dollars per adult ticket

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