See the attached picture.
<span>you are given that ABCE is an isosceles trapezoid. </span>
<span>you are given that AB is parallel to EC. </span>
<span>this means that AE is congruent to BC. </span>
<span>you are given that AE and AD are congruent. </span>
<span>triangle EAD is an isosceles triangle because AE and AD are congruent. </span>
<span>this means that angle 1 is equal to angle 3. </span>
<span>since angle 1 is equal to angle 2 and angle 3 is equal to angle 1, then angle 3 is also equal to angle 2. </span>
<span>this means that AD and BC are parellel because their corresponding angles (angles 3 and 2) are equal. </span>
<span>since AB is parallel to EC and DC is part of the same line, than AB is parallel to DC. </span>
<span>you have AB parallel to DC and AD parallel to BC. </span>
<span>if opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram. </span>
<span>that might be able to do it,depending on whether all these statements are acceptable without proof. </span>
<span>they are either postulates or theorems that have been previously proven. </span>
<span>if not, then you need to go a little deeper and prove some of the statements that you used.. </span>
here's my diagram.
<span>this is not a formal proof, but should give you some ideas about how to proceed. </span>
<span>you can also prove that angle 4 is equal to angle 2 because they are alternate interior angles of parallel lines. </span>
<span>you can also prove that angle 6 is equal to angle 5 because they are alternate interior angles of parallel lines. </span>
Well lets say y = the amount of medals won. lets say x is the amount won by short people and z is the amount won by tall. we know that the total medals is the total medals won by short and tall so:
y = x + z
it says that tall people are 3.times more likely. this would mean they won three times more than short people. so
z = 3x.
so if we know what z equals, we can replace z with what it is equal to. so:
y = x + z
y = x + 3x
y = 4x
we know that 60 medals were won so
y = 4x
60 = 4x
x = 15
that is the amount won by short people
A. The number of 10-boards Peter bought is equal to n divided by 10. Then, each of the 10-boxes will get two boxes of nails. The number of boxes of nails that Peter will have after buying n boards will be,
N = (2)(n/10)
Simplifying,
<em> N = n/5</em>
b. If the number of boards are 90 then,
N2 = (90/10)(2)(100 nails/box)
N2 = 1800
Answer: 1800
1 file + 3 pens = $32.85 --------------- (1)
2 files + 8 pens = $83.50 ----------------(2)
(1) x 2 :
2 files + 6 pens = $65.70 ----------------(1a)
(2) - (1a) :
2 pens = $17.80
1 pen = $8.90
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Answer: One pen costs $8.90.
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