Answer:
Theorem : Opposite sides of a parallelogram are congruent or equal.
Let us suppose a parallelogram ABCD.
Given:AB\parallel CD and BC\parallel AD (According to the definition of parallelogram)
We have to prove that: AB is congruent to CD and BC is congruent to AD.
Prove: let us take two triangles, \bigtriangleup ACD and\bigtriangleup ABC
In these two triangles, \angle1=\angle2 { By the definition of alternative interior angles}
Similarly, \angle4=\angle3
And, AC=AC (common segment)
By ASA, \bigtriangleup ACD \cong \bigtriangleup ABC
thus By the property of congruent triangle, we can say that corresponding sides of \bigtriangleup ACD and \bigtriangleup ABC are also congruent.
Thus, AB is congruent to CD and BC is congruent to AD.
In the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.
<h3>What is the triangle?</h3>
The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
In the first diagram:
The sum of the 5k + 20 and 7k + 40 is 180
5k + 20 + 7k + 40 = 180
12k + 60 = 180
12k = 180 -60
12k = 120
k = 10
In the second diagram:
The sum of the two interior angles is equal to the exterior angle.
40 + 12k + 10 = 8k + 80
4k = 30
k = 30/4 = 15/2
Thus, in the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.
Learn more about the triangle here:
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Answer:
$282.98
Step-by-step explanation:
For computing the principal amount we need to apply the present value function i.e to be shown in the attachment below:
Data provided that in question
Future value = $25,000
Rate of interest = 9%
NPER = 13 years × 4 quarters = 52 quarters
PMT = $0
The formula is shown below:
= -PV(Rate;NPER;PMT;FV;type)
So, after applying the above formula, the present value is $282.98
Recognizing that the dotted line is sin(x) and solid line is cos(x), it's clear to see that the sin(x) has a larger amplitude than cos(x). So, we get a1 > a2.
Only B and E satisfies the above. But E is clearly incorrect since amplitude cannot be less than 0.
Therefore, B would be the correct choice.
