Question

1. This exercise asks you to negate various results that are equivalent to the Euclidean parallel postulate.

(a) Alternate Postulate 5.1. Given a line and a point not on the line, exactly one line can be drawn through the given point and parallel to the given line.

(b) Alternate Postulate 5.2. If two parallel lines
are cut but a transversal, then the alternate interior angles are
equal, each exterior angle is equal to the opposite interior angle,
and sum of the interior angles on the same side of the transversal
is 180^{0}.

(c) Alternate Postulate 5.4. If a straight line intersects one of two parallel lines, it will also intersect the other.

(d) Alternate Postulate 5.9. [Saccheri 3 ( Euclid’s
Proposition I.32 )] The angle sum of any triangle is
180^{0}.

(e) Alternate Postulate 5.11 [Pythagorean Theorem] In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

(f) Alternate Postulate 5.18. [Farkas Bolyai, 1800] Given three noncollinear points, there is a circle passing through all three.

Answer #1

- There exist some line A and some point Q not on the line A such that there doesnot exist a line through Q and parallel to A.
- Two lines are cut by a transversal and alternate interior angles are not equal;each exterior angle is not equal to the opposite interior angles and some of the interior angles on same side of the transversal is not 180 degree
- A straight line intersects one of two parallel lines and doesn't intersects other
- The angle sum of triangle is not 180 degree at all.

A. Explain the connections between geometric constructions and
two of Euclid’s postulates.
1. A straight line segment can be drawn joining any two
points.
2. Any straight line segment can be extended indefinitely in a
straight line.
3. Given any straight line segment, a circle can be drawn having
the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. If two lines are drawn which intersect a third in such a way
that the...

Part 1: Two Round Conductors Gather all items required for the
exercise. Note: If using the lab kit box, remove contents and place
in a secure area. Put on your safety goggles. Center the black
conductive paper on the top of the box, grid-side up. Place the two
metal nuts (conductors) at the (5 cm, 10 cm) and (20 cm, 10 cm)
positions on the paper. Secure using two dissection pins for each
conductor. See Figure 13. Note: Place the...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 24 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago