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Anit [1.1K]
2 years ago
10

The midpoints of an irregular quadrilateral ABCD are connected to form another quadrilateral inside ABCD. Complete the explanati

on of why the quadrilateral is a parallelogram.​
Mathematics
1 answer:
Juliette [100K]2 years ago
5 0

Answer:

Suppose: M, N, P, Q are the midpoints of AB, BC, CD, AD respectively

=> MNPQ is the quadrilateral inside ABCD

connect B to D, ΔABD has : M is the midpoint of AB

                                               Q is the midpoint of AD

=> MQ is the midpoint polygon of ΔABD

=> MQ // BD and MQ = 1/2.BD (1)

ΔBCD has: N is the midpoint of BC

                   P is the midpoint of DC

=> NP is the midpoint polygon of ΔBCD

=> NP // BD and NP = 1/2.BD    (2)

from (1) and (2) => MQ // NP ( //BD)

                             MQ = NP  (=1/2.BD)

=> MNPQ is a parallelogram.​

=>  the quadrilateral inside ABCD is a parallelogram.​

Step-by-step explanation:

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2.2.3 Quiz: Angle Theorems
serious [3.7K]

The value of y is 40 degree , Option B is the correct answer.

<h3>What is Angle Sum Property ?</h3>

According to angle sum property, the sum of all angles of a triangle is equal to 180 degree.

It is given in the question a triangle  , here

the angles given are 2y , y+10 , 50 degree

From the property ,

2y + y +  10 +50 = 180

3y +60 = 180

3y = 120

y = 40 degree

Therefore The value of y is 40 degree , Option B is the correct answer.

To know more about Angle Sum Property

brainly.com/question/4316040

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8 0
2 years ago
Which pair of points have a slope of -3/5?
Allushta [10]

Answer:

No of these answers has a slope of  \frac{-3}{5} . My guess is B becasue its close to \frac{-3}{5} unless the 5 is supposed to be negative

Step-by-step explanation:

You have to use the slope formula \frac{y_{2} - y_{1} }{x_{2} - x_{1} }

(x_{1},y_{1}), (x_{2},y_{2})

(4, 0), (-2, 10)   \frac{10 - 0 }{-2 - 4 }= \frac{10}{6} you have to simplfy, the answer will be \frac{5}{3}

(10, -2), (0, 4)  \frac{4 - -2 }{0- 10 }= \frac{6}{-10} you have to simplfy, the answer will be \frac{3}{-5}

 (4, 2), (10, 4)  \frac{4 - 2 }{10 - 4 }= \frac{2}{6} you have to simplfy, the answer will be \frac{1}{3}

 (-4, -10),(0, -2) \frac{{-2- -10} }{0 - -4 }= \frac{8}{4} you have to simplfy, the answer will be \frac{2}{1} =2

5 0
2 years ago
What are the 2 ways to make 10's and ones out of 28 cubes
andriy [413]
I'm sorry my friend but I need as much help as you do I'm just answering this so I can get some help sorry
8 0
3 years ago
At what point do the lines y = 6x – 18 and<br> y=8x – 32 intersect?
anzhelika [568]

Answer:

(7, 24)

Step-by-step explanation:

Solve the system:

6x - 18 = 8x - 32

2x = 14

x = 7

y = 6(7) - 18

y = 24

4 0
2 years ago
You want to put a 5 inch thick layer of topsoil for a new 23 ft by 18 ft garden. the dirt store sells by the cubic yards. how ma
lianna [129]

5 inches = 5/12 = 0.4166 feet

23 x 18 x 0.4166 = 172.5 cubic feet

1 cubic foot = 0.037037 cubic yards

172.5 x 0.037037 = 6.39 round up to 6.5 cubic yards

5 0
3 years ago
Read 2 more answers
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