By CK-12 Foundation
CK-12's easy Geometry FlexBook, Volumes 1 via 2, is designed to give scholars with geometric rules in a extra graphics-oriented path. quantity 1 contains 6 chapters: fundamentals of Geometry, Reasoning and evidence, Parallel and Perpendicular strains, Triangles and Congruence, Relationships with Triangles, and Polygons and Quadrilaterals.
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Additional info for CK-12 Basic Geometry, Volume 1 of 2
This is the definition of an obtuse angle. All geometric definitions are biconditional statements. Example 7: a) Is true? If not, find a counterexample. b) Is true? If not, find a counterexample. c) Is true? If not, find a counterexample. d) Is true? If not, find a counterexample. Solution: a) If , then . True. b) If , then . False, c) If , then . False, d) If , then . True, Know What? Revisited The series of events is as follows: If the man raises his spoon, then it pulls a string, which tugs the spoon back, then it throws a cracker into the air, the bird will eat it and turns the pedestal.
With measurement, we put an in front of the sign to indicate measure. So, and . Just like the Ruler Postulate for line segments, there is a Protractor Postulate for angles. Protractor Postulate: For every angle there is a number between and that is the measure of the angle. The angle's measure is the difference of the degrees where the sides of the angle intersect the protractor. For now, angles are always positive. In other words, you do not have to start measuring an angle at , as long as you subtract one measurement from the other.
Questions 20-25 use the definitions, postulates and theorems in this section. For questions 1-6, classify each triangle by its sides and by its angles. Can you draw a triangle with a right angle and an obtuse angle? Why or why not? In an isosceles triangle, can the angles opposite the congruent sides be obtuse? In problems 9-14, name each polygon in as much detail as possible. Explain why the following figures are NOT polygons: How many diagonals can you draw from one vertex of a pentagon? Draw a sketch of your answer.