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mixas84 [53]
3 years ago
11

Justify why a/b x b/c x c/d x d/ e is equal to a/e when b,c,d, and e are not zero?

Mathematics
1 answer:
Nuetrik [128]3 years ago
5 0
When you multiply fractions, you multiply across, right? so, for example 5/7 times 4/9 will give you 20/63. So, if you do this to this problem, you will have abcd/bcde. but now you are able to cancel out the b and c and d. think of it like reducing. 5/10 is 1/2. Why? because if you reduce/factor out a 5, you get a 1 in the numerator and a 2 in the denominator. same thing here; you can factor out a b, c, and d(because they show up in both num. and denom. so what you are left with is a/e. Cheers!
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Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-c
natali 33 [55]

Answer:  By the slope formula.

Step-by-step explanation:

Given: ABC is a triangle (shown below),

In which A≡(6,8), B≡(2,2) and C≡(8,4)

And, D and E are the mid points of the line segments AB and BC respectively.

Prove: DE║AC and DE = AC/2

Proof:

Since, And, D and E are the mid points of the line segments AB and BC respectively.

Therefore, By mid point theorem,

coordinate of D are (\frac{2+6}{2} , \frac{2+8}{2} ) = (\frac{8}{2} , \frac{10}{2} )= (4,5)

Coordinate of E are  (\frac{2+8}{2} , \frac{2+4}{2} ) = (\frac{10}{2} , \frac{6}{2} )= (5,3)

By the distance formula,

DE=\sqrt{(5-4)^2+(3-5)^2}=\sqrt{5}

AC=\sqrt{(8-6)^2+(4-8)^2}=2\sqrt{5}

By the slope formula,

Slope of AC = \frac{4-8}{8-6} = \frac{-4}{2} = -2

Slope of DE =  \frac{3-5}{5-4} = \frac{-2}{1} = -2


            Statement                                              Reason

1. The coordinate of D are (4,5)  and           1. By the midpoint formula

the coordinate of  E are (5,3)

2. The length of DE = √5                            2. By the Distance formula

The length AC = 2√5 ⇒ Segment DE

is half the length of segment AC

3. The slope of DE = -2 and the                3. By the slope formula

slope of AC = -2

4. DE║AC                                                   4. Slopes of parallel lines are equal


7 0
3 years ago
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