going thru Geometry basics and I'm stuck just understanding the basics.  This doesn't bode well for the year...
Anyway, can someone please explain the following statements:
The statement 'Three points all lie in each of two planes' is true but the statement 'Three noncollinear points all lie in each in each of two planes' is false.
Please explain this.  I think of 3 random points.  I would think 2 could be in one plane and 1 could be in another plane.  Yet Postulate 7 says specifically '... and through any 3 noncollinear points there is exactly one plane.'  Why?  In my mind I'm still thinking of 3 random points.  What is the difference?
in Geometry Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Two points are always colinear, but a third point is not necessarily on a line joining or passing through the other two points. Imagine the two points forming part of the edge of a plane. Using the line joining them as a hinge the plane can be moved so as to uniquely include the third point, so the points are then coplanar. One plane includes all three points, and it is the only plane to do so.

Going back to each of the two points, call them A and B, the third point C can be joined by a line so A and C can be on a separate plane from the plane that contains A and B. Similarly, a second plane can contain B and C. So we have four configurations: one plane containing all three points and three different planes each containing a pair of points: AB and AC, AB and BC, and AC and BC. So the three non-colinear points (not all three are in line, but two out of three must be) don't all lie on the same two planes: a pair of points only lies on each of the two planes, the third point shares a plane with only one of the other points.

Does that seem clearer?

 

by Top Rated User (1.1m points)

Related questions

1 answer
asked Aug 21, 2012 in Geometry Answers by anonymous | 1.5k views
1 answer
1 answer
asked Dec 15, 2020 in Geometry Answers by anonymous | 273 views
1 answer
asked Feb 23, 2013 in Geometry Answers by anonymous | 515 views
1 answer
asked May 31, 2014 in Other Math Topics by trex Level 1 User (120 points) | 427 views
1 answer
asked May 23, 2015 in Geometry Answers by florie | 971 views
1 answer
asked Feb 13, 2013 in Geometry Answers by anonymous | 901 views
0 answers
1 answer
asked Jul 21, 2013 in Geometry Answers by Alexa | 367 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages math problem geometry problems calculus problems math fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations probability algebra pre algebra problems word problem evaluate the expression slope intercept form statistics problems factoring polynomials solving inequalities 6th grade math how to find y intercept equation of a line sequences and series algebra 2 problems logarithmic equations solving systems of equations by substitution dividing fractions greatest common factor square roots geometric shapes graphing linear equations long division solving systems of equations least to greatest dividing decimals substitution method proving trigonometric identities least common multiple factoring polynomials ratio and proportion trig identity precalculus problems standard form of an equation solving equations with fractions http: mathhomeworkanswers.org ask# function of x calculus slope of a line through 2 points algebraic expressions solving equations with variables on both sides college algebra domain of a function solving systems of equations by elimination differential equation algebra word problems distributive property solving quadratic equations perimeter of a rectangle trinomial factoring factors of a number fraction word problems slope of a line limit of a function greater than or less than geometry division fractions how to find x intercept differentiation exponents 8th grade math simplifying fractions geometry 10th grade equivalent fractions inverse function area of a triangle elimination method story problems standard deviation integral ratios simplify systems of equations containing three variables width of a rectangle percentages area of a circle circumference of a circle place value solving triangles parallel lines mathematical proofs solving linear equations 5th grade math mixed numbers to improper fractions scientific notation problems quadratic functions number of sides of a polygon length of a rectangle statistics zeros of a function prime factorization percents algebra 1 evaluating functions derivative of a function equation area of a rectangle lowest common denominator solving systems of equations by graphing integers algebra 2 diameter of a circle dividing polynomials vertex of a parabola calculus problem perpendicular lines combining like terms complex numbers geometry word problems converting fractions to decimals finding the nth term range of a function 4th grade math greatest to least ordered pairs functions radius of a circle least common denominator slope unit conversion solve for y calculators solving radical equations calculate distance between two points area word problems equation of a tangent line multiplying fractions chemistry binomial expansion place values absolute value round to the nearest tenth common denominator sets set builder notation please help me to answer this step by step significant figures simplifying radicals arithmetic sequences median age problem trigonometry graphing derivatives number patterns adding fractions radicals midpoint of a line roots of polynomials product of two consecutive numbers limits decimals compound interest please help pre-algebra problems divisibility rules graphing functions subtracting fractions angles numbers discrete mathematics volume of a cylinder simultaneous equations integration probability of an event comparing decimals factor by grouping vectors percentage expanded forms rational irrational numbers improper fractions to mixed numbers algebra1 matrices logarithms how to complete the square mean statistics problem analytic geometry geometry problem rounding decimals 5th grade math problems solving equations with variables solving quadratic equations by completing the square simplifying trigonometric equation using identities
87,441 questions
99,039 answers
2,422 comments
16,938 users