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

First and second order derivative, Solution : We'll require the first and s...

Solution : We'll require the first and second derivative to do that. y'(x) = -3/2x -5/2                                     y''(x) = 15/4x -7/2 Plug these and also the funct

Find out the volume of the solid- method of rings, Find out the volume of t...

Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and  y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t

Find the value of the derivative, Given y = f(x) = x 2 + 2x +3 a) Use the ...

Given y = f(x) = x 2 + 2x +3 a) Use the definitional formula given below to find the derivative of the function. b) Find the value of the derivative at x = 3.

Satistics, I have about 6 Statistics questions, can anyone help me?

I have about 6 Statistics questions, can anyone help me?

Differentiation, how to write assignment of the application of differentiat...

how to write assignment of the application of differentiation in science

Matrix equation , Hi may i know how to substract the (ID)colum matrix from ...

Hi may i know how to substract the (ID)colum matrix from (K)square matrix as per equation below. E = (K - ID)^-1 S K is m*m matrix I is idntity matrix d is column vector s is col

Right angle triangle, If the points for a right angle triangle are XYZ wher...

If the points for a right angle triangle are XYZ where do I mark the points?

How many packets of the first type did she purchase, The manager of a garde...

The manager of a garden store ordered two different types of marigold seeds for her display. The first type cost her $1 per packet and the second kinds cost $1.26 per packet. How m

Rectilinear figures, what are rctilinear figures ? types of rectilinear fig...

what are rctilinear figures ? types of rectilinear figures and their propertiees.

Solving algebraic word problems, Solving Algebraic Word Problems: What...

Solving Algebraic Word Problems: What are the capacities of two water storage tanks in a nuclear facility if one holds 9 gallons less than three times another, and their whole

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