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Andrew [12]
1 year ago
9

I really am confused on how to write a proof.

Mathematics
1 answer:
kvasek [131]1 year ago
8 0

Since ABCD is a parallelogram, the opposite sides will be parallel and equal,

\begin{gathered} AB=CD \\ BC=AD \end{gathered}

Consider that AC acts as a transversal to the parallel lines AB and CD, so we can write,

\begin{gathered} \angle CAD=\angle ACB\text{ (Alternate Interior Angles)} \\ BC=AD\text{ (Opposite sides of parallelogram)} \\ \angle ADB=\angle CBD\text{ (Alternate Interior Angles)} \end{gathered}

So by the ASA criteria, the triangle AED is congruent to the triangle CEB,

Then the corresponding parts of the triangles will be equal,

\begin{gathered} AE=CE \\ BE=DE \end{gathered}

Hence Proved.

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My brain stopped. Please help
Over [174]

Answer:

∠1 = 90°

∠2 = 66°

∠3 = 24°

∠4 = 24°

Step-by-step explanation:

Usually the diagonals of a rhombus bisect each other at right angles.

Thus; ∠1 = 90°

Since they bisect at right angles, then;

∠R1S = 90°

Now, sum of angles in a triangle is 180°

Thus;

66° + 90° + ∠4 = 180°

156 + ∠4 = 180

∠4 = 180 - 156

∠4 = 24°

Now, also in rhombus, diagonals bisect opposite angles.

Thus; ∠4 = ∠3

Thus, ∠3 = 24°

Similarly, the diagonal from R to T bisects both angles into 2 equal parts.

Thus; ∠2 = 66°

6 0
2 years ago
A boat traveled 280 miles downstream and back. The trip downstream took 7 hours. The trip back took 14 hours. Find the speed of
katrin2010 [14]
Downstream 280mi/7 hours
(Speed =change in position/change in time)
40mi/hr
Back
280/14
20mi/hr
5 0
3 years ago
Monica bought 14.75 yards of muslin
nikdorinn [45]

Answer: 531 inches

Step-by-step explanation:

3 0
2 years ago
a collector has 80 jackeys and 125 shirts she wants to maintain ratio in her collection but she needs to sell some of her items
Irina18 [472]

Answer:

25

Step-by-step explanation:

Well, we need to simplify this. we have a ratio of 80:125.

As these numbers end in either 0 or 5, we know they are divisible by 5.

By dividing these by five, our ratio becomes 16:25.

As we have 16 jackets, we know we must need to sell 25 jackets to maintain the ratio.

8 0
3 years ago
The Ford family decides they want to go see a movie at the local movie theater. The family consists of two adults, and five chil
Brrunno [24]

Ford Family consists of:

a) 2 adults

The price of ticket for each adult is $18.55. This can be approximated to $19 if we round it to nearest dollar. So the price of ticket for 2 adults will be 2 x 19 = $38

b) 3 children between ages 2 and 10.

Ticket for each child between ages 2 - 10 is $12.59 which can be approximated to $13. So ticket price for 3 children will be 3 x 13 = $39

c) 2 children below the age of 2.

Ticket price for each child is $6.54 which can approximated as $7. So ticket price for 2 children will be 2 x 7 = $14

The estimated total amount due on the family equals = 38 + 39 + 14 = $91

In each of the 3 cases we rounded up the values. So this means the actual amount must be slightly lesser than $91. The actual bill was $87.95 which is close to $91 and lesser than it. Hence we can conclude that $87.95 is the correct amount due for Ford Family.

3 0
3 years ago
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