Question

In: Advanced Math

Let l and m be two lines in ordinary Euclidean geometry intersecting at point O. Let...

Let l and m be two lines in ordinary Euclidean geometry intersecting at point O. Let A, B and C be three distinct points on l and A', B' and C' three distinct points on m (none of them equal to O). Suppose that AB' is parallel to BA', and AC' is parallel to CA'. Prove, using Pappus' theorem in the Extended Euclidean Plane, that BC' and CB' are parallel.

Solutions

Expert Solution

The Pappus' theorem in Extended Euclidean plane given as,

The Proof is Given Below:


Related Solutions

The chainage of the intersecting point (P.I.) of two straight lines is 4227.463m. The Whole-Circle- Bearing...
The chainage of the intersecting point (P.I.) of two straight lines is 4227.463m. The Whole-Circle- Bearing of two straight lines (in and out) are 111o 36' 33.3" and 116o 35' 01.6" respectively. A simple curve with radius 1000.00m to connect to two straight lines. Calculate the setting-out information by deflection angle method at 20.0m continuous chainages in table form.
Determine whether the following two lines are parallel, intersecting, or skew. If they are skew, find...
Determine whether the following two lines are parallel, intersecting, or skew. If they are skew, find the distance between them L1 : x = 3 + 2t, y = 4 − 3t, z = −1 − 4t and L2 : 1 + 2s, y = 2 + s, z = 3 + 2s
Determine whether the following two lines are parallel, intersecting, or skew. If they are skew, find...
Determine whether the following two lines are parallel, intersecting, or skew. If they are skew, find the distance between them L1 : x = 3 + 2t, y = 4 − 3t, z = −1 − 4t and L2 : 1 + 2s, y = 2 + s, z = 3 + 2s
Give a proof by contradiction to show that if two lines l and m are cut...
Give a proof by contradiction to show that if two lines l and m are cut by a transversal in such a way that the alternate interior angles, x and y, have the same measure, then the lines are parallel. Write the "if, then" statement for the proof by contradiction and the proof.
In Schwarzschild geometry, the distance between two circles with different circumferences is larger than the Euclidean...
In Schwarzschild geometry, the distance between two circles with different circumferences is larger than the Euclidean result, because the distance between the two circles is given by integrating dr/ (1 − rs/r) (where rs is a positive constant) along the radial path between them. Invent an embedding of the radial part of the Schwarzschild spatial geometry in one extra Euclidean dimension, that we will call the z dimension. What is the relationship between dr and dz of the one-dimensional “surface”...
Prove that, in hyperbolic geometry, for each point P and a line l not containing P,...
Prove that, in hyperbolic geometry, for each point P and a line l not containing P, there are infinitely many lines through P parallel to l.
Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that...
Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that the distance from one line to another cannot have the same value in more than two places. Please prove geometrically, not algebraically.
Let INFINITE PDA = {<M>|M is a PDA and L(M) is an infinite language}. Show that...
Let INFINITE PDA = {<M>|M is a PDA and L(M) is an infinite language}. Show that INFINITE PDA is decidable.
Let S={1,2,3,6} and define the relation ~ on S2 by (m,n) ~ (k,l) for m+l=n+k Show...
Let S={1,2,3,6} and define the relation ~ on S2 by (m,n) ~ (k,l) for m+l=n+k Show that it is an equivalent relation Find the number of different equivalent classes and write all of them
A mechanical aim rotates in the vertical plan about point O. The slider P (m =...
A mechanical aim rotates in the vertical plan about point O. The slider P (m = 2 kg) is drawn toward O with a constant speed (?̇) of 0.5 m/s through the rough slot (friction coefficient µ = 0.1) by pulling on the free end E of the cord. At the instant when r = 0.25 m, the arm is rotating with a constant speed (?̇) of 10 rad/s in the clockwise direction. When the slider is oriented at an...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT