1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
In-s [12.5K]
3 years ago
13

Given: The coordinates of triangle PQR are P(0, 0), Q(2a, 0), and R(2b, 2c).

Mathematics
1 answer:
masha68 [24]3 years ago
6 0

Answer:

The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down

Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

  problem

- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is

  (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

* Lets solve the problem

- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)

- Lets find the mid-poits of PQ called A

∵ Point P is (x1 , y1) and point Q is (x2 , y2)

∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0

∵ A is the mid-point of PQ

∴ A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)

- Lets find the mid-poits of PR which called B

∵ Point P is (x1 , y1) and point R is (x2 , y2)

∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c

∵ B is the mid-point of PR

∴ B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)

- The parallel line have equal slopes, so lets find the slopes of AB and

  QR to prove that they have same slopes then they are parallel

# Slope of AB

∵ Point A is (x1 , y1) and point B is (x2 , y2)

∵ Point A = (a , 0) and point B = (b , c)

∴ x1 = a , x2 = b and y1 = 0 and y2 = c

∴ The slope of AB is m=\frac{c-0}{b-a}=\frac{c}{b-a}

# Slope of QR

∵ Point Q is (x1 , y1) and point R is (x2 , y2)

∵ Point Q = (2a , 0) and point R = (2b , 2c)

∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c

∴ The slope of AB is m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}

∵ The slopes of AB and QR are equal

∴ AB // QR

∵ AB is the line containing the midpoints of PQ and PR of Δ PQR

∵ QR is the third side of the triangle

∴ The line containing the midpoints of two sides of a triangle is parallel

  to the third side

You might be interested in
What is the value of x?
Andrew [12]

Answer:

45??

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What's the recommend amount of UV protection that sunglasses should provide?
BabaBlast [244]
They should screen out 99 to 100 percent of uv rays. Hope this helps!
7 0
3 years ago
Read 2 more answers
HELPP YALL! ILL MARK BRAINIEST!!!
olga55 [171]

Answer:

Hi first can u mark me brainiest

Step-by-step explanation:

8 0
3 years ago
I need to find the surface area of this box. Will someone help me?
Jlenok [28]

Answer: 480. Hope it helps! :)

Step-by-step explanation:first, you times 10 times 8, you get 80. then, you times it by six. Your answer is 480.

6 0
3 years ago
Help ASAP please
mr Goodwill [35]

Answer:

19cm

Step-by-step explanation:

x * 5x = 1805

5x ^2 = 1805

x^2 = 361

square root of that is 19

5 0
3 years ago
Read 2 more answers
Other questions:
  • Suppose that a car normally sells for $16,500 and is now on sale for $14,000. What is the percent of discount?
    6·1 answer
  • Solve for perimeter and area of rectangle
    12·1 answer
  • How do you simplify, distribute and combine like terms?
    9·1 answer
  • What will be the measure of exterior angle of regular pentagon give reason of you answer
    9·1 answer
  • Find f( 2 ) , f( 3 ) , f( 4 ) , and f( 5 ) if f is defined recur-sively by f( 0 ) = f( 1 ) = 1 and for n = 1 , 2 ,... a) f(n + 1
    6·1 answer
  • Drag the numbers to create three ratios that are equivalent to 4:12.
    5·2 answers
  • Sarah makes 1/2 pound of caramel popcorn and puts it in a bag that holds 1/8 of a pound. Which equation can be used to find how
    7·1 answer
  • 6. The sum of two numbers is 30. The sum of the
    7·1 answer
  • How can you find 50% of any number? Select all that apply.
    11·2 answers
  • I don’t how to do these does anybody know how?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!