Which of the following are among the five basic postulates of euclidean geometry? check all that apply a. a straightedge and compass can be used to create any figure. b. the angles of a triangle always add up to 180 degrees c. a straight line segment can be drawn between any two points d. any straight line segment can be extended indefinitely

Answer with explanation:

Postulates or Axioms are universal truth statement , whereas theorem requires proof.

Out of four options given ,the following are basic postulates of euclidean geometry:

Option C: A straight line segment can be drawn between any two points.

   →To draw a straight line segment either in space or in two dimensional plane you need only two points to determine a unique line segment.

Option D: any straight line segment can be extended indefinitely

 →Yes ,a  line segment has two end points, and  you can extend it from any side to obtain a line or new line segment.

We need other geometrical instruments , apart from straightedge and compass  to create any figure like, Protractor, Set Squares.

So, Option A is not Euclid Statement.

Option B , is a theorem,which is the angles of a triangle always add up to 180 degrees,not a Euclid axiom.

→Option C, and Option D

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

irrational, cannot