Extrakt04

2022-06-25

Lorenz, Every single line through a point within an angle will meet at least one side of the angle.

I know I have to Show that the parallel postulate 5 implies lorenz, and then lorenz implies parallel postulate 5.

Assume postulate 5 . So we are given AB and a point C not on AB. Choose B on AB draw CD to construct angle ECD= angle BDC.

I just don't get what Lorenz postulate means. Thats where I am getting stuck.

I know I have to Show that the parallel postulate 5 implies lorenz, and then lorenz implies parallel postulate 5.

Assume postulate 5 . So we are given AB and a point C not on AB. Choose B on AB draw CD to construct angle ECD= angle BDC.

I just don't get what Lorenz postulate means. Thats where I am getting stuck.

Aaron Everett

Beginner2022-06-26Added 18 answers

HINT Suppose Lorenz Postulate is false in the Presence of the 5th postulate and reach a contradiction.

Suppose Lorenz Postulate is true and the 5th Postulate is false and reach a contradiction.

Suppose Lorenz Postulate is true and the 5th Postulate is false and reach a contradiction.

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola $A)\frac{\sqrt{5}}{4}\phantom{\rule{0ex}{0ex}}B)\frac{\sqrt{7}}{4}\phantom{\rule{0ex}{0ex}}C)\frac{7}{4}\phantom{\rule{0ex}{0ex}}D)\frac{5}{3}$

Which of the following is an example of a pair of parallel lines?

Sides of a triangle

Surface of a ball

Corner of a room

Railway trackState whether the statements are True or False. All rectangles are parallelograms.

Point T(3, −8) is reflected across the x-axis. Which statements about T' are true?

If two parallel lines are cut by a transversal, then:

each pair of alternate angles are equal

each pair of alternate angles add up to 180 degrees

each pair of corresponding angles add up to 180 degees.

each pair of corresponding angles is equal.The opposite faces of a dice always have a total of ___ on them.

What is the term for a part of a line with two endpoints?

A. Line Segment

B. Line

C. Ray

D. PointABCD is a parallelogram. Which of the following is not true about ABCD?

AB=CD

AD=CB

AD||CD

AB||CDIf the points $(a,0)$, $(0,b)$ and $(1,1)$ are collinear then which of the following is true?

$\frac{1}{a}+\frac{1}{b}=1$

$\frac{1}{a}-\frac{1}{b}=2$

$\frac{1}{a}-\frac{1}{b}=-1$

$\frac{1}{a}+\frac{1}{b}=2$The angles of a triangle are in the ratio 1 : 1 : 2. What is the largest angle in the triangle?

$A){90}^{\circ}\phantom{\rule{0ex}{0ex}}B){135}^{\circ}\phantom{\rule{0ex}{0ex}}C){45}^{\circ}\phantom{\rule{0ex}{0ex}}D){150}^{\circ}$What is the greatest number of acute angles that a triangle can contain?

How many right angles are required to create a complete angle?

1) Two

2) Three

3) Four

4) FiveFind the sum of interior angles of a polygon with 12 sides in degrees.${1800}^{\circ}\phantom{\rule{0ex}{0ex}}{1200}^{\circ}\phantom{\rule{0ex}{0ex}}{1500}^{\circ}\phantom{\rule{0ex}{0ex}}{1400}^{\circ}$

In Euclid's Division Lemma when $a=bq+r$ where $a,b$ are positive integers then what values $r$ can take?

When two lines cross each other at a point we call them ___ lines.