1-3 Collinearity and assumptions

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Presentation transcript:

1-3 Collinearity and assumptions

. . . . . Collinear: Points that are on the same line. Noncollinear: Points NOT on the same line. . . . . .

Draw one diagram with the following conditions: A, B, and C are collinear A, D, and E are collinear B, C, and D are noncollinear

Betweenness: In order for us to say a point is between two other points, ALL three points must be collinear. ______ is between A and B.

Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle are greater than the length of the third. 3 5 4 3 + 4 > 5 4 + 5 > 3 https://www.mathsisfun.com/geometry/triangle-inequality-theorem.html

General rules to follow when getting information from a diagram You Should Assume You Should NOT Assume Straight lines and Angles Right Angles Collinearity of Points Congruent Segments Betweeness of Points Congruent Angles Relative Position of Points Relative size of segments and angles

What should we assume about the given diagram? Do Assume Do Not Assume C B A Do Assume Do Not Assume , are straight lines is a right angle is a straight angle C, D, and E are noncollinear C is between B and E is an obtuse angle D is to the right of C is longer than