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Technically this does not exist. Many math texts use it as a shortcut to introduce properties of angles for parallel lines that are cut by a transversal.
It says that when lines are parallel and are cut by a transversal, then the same side interior angles must be supplementary (add up 180 degrees).
Once you say this is a postulate (assumed to be true), then you can prove other things like the Congruent Corresponding Angles theorem that says "If lines are parallel and are cut by a transversal, then the corresponding angles must be conguent."
Some texts do the reverse and say Corresponding Angles is a postulate and then prove Same-Side Interior as a Theorem.
Euclid proved both these using his 5th Postulate (often re-written as the Parallel Postulate or Playfair's Axiom). To do this, he had to prove that the interior angles of a triangle sum to 180. Since many Math Texts do not introduce this fact until later chapters, they take this shortcut of "assume the Same-Side Interior" is true and the remaining theorems are much easier. Another reason Math books may take this shortcut is that Euclid's method is usually done by proof by contradiction - which is sometimes more difficult to understand.
I believe the Khan Academy video of this material is done correctly.
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Why the measure of exterior angles is equal to the sum of the measures of interior opposite angles?
That is only true of triangles and is a consequence of the parallel postulate. In fact it is an alternative way of stating Euclid's parallel postulate.
Does the ocean have seasons?
yes through the vertical angles according to the Postulate 16 concluding that the Alternate Interior angles deduct this...
Does euclid 5th postulate imply existence of parallel linesexplain?
Yes by one definition of interior angles - it does !
What are not a postulate of Euclidean geometry?
Answer to this: All equilateral triangles have interior angles equal to 60 degrees APEX
What is the fifth postulate of Euclid's?
The parallel postulate: "That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."
Why does a triangle have 180 degree?
It is a consequence of Euclid's parallel postulate. In fact, in some versions, the statement that "a plane triangle has interior angles that sum to 180 degrees" replaces the parallel postulate.
What is the linear pair postulate?
1. Where the angles in a linear pair are supplementry, and if parallel lines are cut by a transversal, then the interior angles are congruent, and if two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel. That's what makes up a linear pair postulate anyway. 2. If two adjacent angle's unshared sides form a straight angle, then they are a linear pair. 3.If two angles form a linear pair,then they are supplementary.
What saa congruence postulate?
SAA Congruence Postulate states that if two angles and a side opposite one of the angles are the same, the triangles are congruent.
Where does the formula for the sum of interior angles of a polygon come from?
Euclid parallel postulate can be interpreted as being equivalent to the sum of the angles of a [plane] triangle being 180 degrees. It is quite easy to prove that a polygon with n sides can be divided into n triangles. Putting the two together, you get the formula for the sum of the interior angles of a polygon.
What is Supplement Postulate?
The Supplement Postulate states that if two angles form a linear pair, then they are supplementary.
What is the difference between a ruler postulate and a protractor postulate?
a ruler measures the distance and a protractor measures the angles
What is Asa congruence postulate?
Angle side angle congruence postulate. The side has to be in the middle of the two angles
