Given: Parallelogram KLMN
2 answers:
Answer:
It is followed by properties of parallelogram and the proof is explained in step-by-step solution.
Step-by-step explanation:
Given a parallelogram KLMN
Parallelogram is a quadrilateral with parallel opposite sides.
To Prove: ∠N≅∠L and ∠M≅∠K
In Parallelogram KLMN the opposite sides are parallel therefore, the opposite angles are vertical angles. And the vertical angles are always equal and congruent. Hence,
∠N≅∠L and ∠M≅∠K
For any quadrilateral sum of all angles equal to 360°
m∠K + m∠L + m∠M + m∠N = 360°
Now given quadrilateral is parallelogram therefore opposite angles are equal. So, we can write m∠L = m∠N, m∠M = m∠K
⇒ m∠K + m∠N + m∠K + m∠N = 360°
2 m∠K + 2 m∠N = 360°
m∠K + m∠N = 180°
For the same parallelogram, because opposite sides are equal therefore use m∠K = m∠L, m∠N = m∠M using above equation, we get
m∠L + m∠M = 180°
Because m∠M = m∠K
m∠K + m∠L = 180°
Same Side Interior Angles Theorem states that if the two parallel lines intersect or cut by a transversal then the interior angles on the same side are supplementary that means their sum is equal to 180°
Hence, by above theorem m∠K + m∠N = 180°
& m∠K + m∠L = 180°
By above two equations, we get
m∠K + m∠N = m∠K + m∠L
because m∠K = m∠M & ∠N = ∠L
⇒ m∠L + m∠M = m∠K + m∠L
Because opposite angles of a parallelogram are alternate angles therefore are equal. hence,
m∠N = m∠L
m∠M = m∠K
Angle congruency postulate
Opposite angles of parallelogram are vertical angles and the vertical angles are congruent as well as equal.
∠N≅∠L and ∠M≅∠K
Substitution Property of equality states that if one angle is equal to another angle the one can be substituted in the place of another that means if ∠M=∠K then we can substituted ∠K in place of ∠M
Transitive property of congruence states that if if the two angles or segments or triangles are congruent to third then they are congruent to each other.
Subtraction Property of Equality states that if if two sides of any equation are equal then subtraction of same value from both sides results in equality of equation.
Parallel lines are those lines which do not intersect or cut each other at the end.
Parallelogram is a quadrilateral have opposite sides equal and parallel.
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Step-by-step explanation:
Assuming the value for the mean 79 and the deviation 8.8
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Part a
Let X the random variable that represent the amount of collagen of a population, and for this case we know the distribution for X is given by:
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If we apply this formula to our probability we got this:
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3) Part b
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If we apply this formula to our probability we got this:
And we can find this probability on this way:
4) Part c
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And we can find this probability on this way:
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