Problem: Given points A and B, draw a line passing through both points.
Solution: Using a straightedge, draw a line connecting points A and B. By the postulate, this line is determined by the two points.
Example problem involving a theorem:
Theorem: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Problem: Given a right triangle with legs of length 3 and 4 units, find the length of the hypotenuse.
Solution: Using the Pythagorean theorem, we have:
h^2 = 3^2 + 4^2
h^2 = 9 + 16
h^2 = 25
h = 5
Therefore, the length of the hypotenuse is 5 units.
Answers & Comments
Answer:
Example problem involving a postulate:
Postulate: Two points determine a line.
Problem: Given points A and B, draw a line passing through both points.
Solution: Using a straightedge, draw a line connecting points A and B. By the postulate, this line is determined by the two points.
Example problem involving a theorem:
Theorem: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Problem: Given a right triangle with legs of length 3 and 4 units, find the length of the hypotenuse.
Solution: Using the Pythagorean theorem, we have:
h^2 = 3^2 + 4^2
h^2 = 9 + 16
h^2 = 25
h = 5
Therefore, the length of the hypotenuse is 5 units.