What is congruent angles in parallel lines, Mathematics

Assignment Help:

What is Congruent Angles in Parallel Lines ?

Postulate 4.1 (The Parallel Postulate)

Through a given point not on a line there is exactly one line parallel to the line.

Theorem

If two parallel lines are cut by a transversal, each pair of alternate interior angles are congruent.

Given: and intersects at P
Prove: 1 @ 2
Proof: (indirect proof)

Assume m1  m2. Then we can draw another line through P such that the 3 formed by and is congruent to 2. From Theorem 4.1, // . That means is parallel to two lines in the plane at point P. This violates the Parallel Postulate. So we conclude that our assumption is false. Therefore, 1 @ 2

 


Related Discussions:- What is congruent angles in parallel lines

Show that the vector is in the perfect matching polytope, 1.  Let G = (V,E)...

1.  Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected. a) Show that the vector x which is indexed by the edges E and for which x e =

Show that the height of the opposite house, From a window x meters hi...

From a window x meters high above the ground in a street, the angles of elevation and depression of the top and the foot of the other house on the opposite side of the street  are

Prove that if x is a real number then [2x] = [x] + [x + ½ ], Prove that if...

Prove that if x is a real number then [2x] = [x] + [x + ½ ] Ans: Let us consider x be any real number. It comprises two parts: integer and fraction. With no loss of

Harmonic progression (h.p.), Three quantities a, b and c are said to ...

Three quantities a, b and c are said to be in harmonic progression if, In this case we observe that we have to consider three terms in o

PROBLEM SOLVING, The perimeter of a rectangular swimming pool is 60m. The l...

The perimeter of a rectangular swimming pool is 60m. The length of the pool is 4 m more than the width. What is the width of the pool?

Simple interest, write a program C++ programming language to calculate sim...

write a program C++ programming language to calculate simple interest, with it algorithm and it flowchart

Complex eigenvalues, It is the last case that we need to take a look at. Th...

It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system, x?' = A x? Here the eigenvalues of the matrix A are compl

Geometry, what shapes can go into a triangular prism

what shapes can go into a triangular prism

Triangle treat, what letters to fill in the boxes

what letters to fill in the boxes

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd