Additionally, all intersections form a 90 ∘ 90 ∘ angle. The grid also tells us that the vertical lines are parallel and the horizontal lines are parallel. Because they are on a grid, we assume all lines are equally spaced across the grid horizontally and vertically. The third way would be the most efficient way.ĭrawing these lines on a grid is the best way to distinguish which pairs of lines are parallel and which are perpendicular. From school to the post office or dry cleaners to home: first way A E ¯, E F ¯, F C ¯, C D ¯, D G ¯ A E ¯, E F ¯, F C ¯, C D ¯, D G ¯ second way A B ¯, B E ¯, E F ¯, F C ¯, C D ¯, D G ¯ A B ¯, B E ¯, E F ¯, F C ¯, C D ¯, D G ¯ third way A B ¯, B C ¯, C F ¯, F G ¯ A B ¯, B C ¯, C F ¯, F G ¯.The first way should be the most efficient way. From school to the library: first way A E ¯, E F ¯, F G ¯ A E ¯, E F ¯, F G ¯ second way A B ¯, B C ¯, C D ¯, D G ¯ A B ¯, B C ¯, C D ¯, D G ¯ third way A B ¯, B E ¯, E F ¯, F G ¯ A B ¯, B E ¯, E F ¯, F G ¯ fourth way A B ¯, B C ¯, C F ¯, F G ¯ A B ¯, B C ¯, C F ¯, F G ¯.

It seems that the third way is the most efficient way. From school to the grocery store and home: first way A H ¯, H I ¯, I E ¯, E F ¯, F G ¯ A H ¯, H I ¯, I E ¯, E F ¯, F G ¯ second way A B ¯, B E ¯, E I ¯, I E ¯, E F ¯, F G ¯ A B ¯, B E ¯, E I ¯, I E ¯, E F ¯, F G ¯ third way A E ¯, E I ¯, I E ¯, E F ¯, F G ¯ A E ¯, E I ¯, I E ¯, E F ¯, F G ¯.Which way do you think is the most efficient way to walk, get your errands done, and go home? Name three ways you might walk to do your errands and end up at home. Suppose you need to go to the post office and the dry cleaners on your way home from school.How about stopping at the library after school? Name four ways you might travel to the library and which way do you think is the most efficient?.In other words, name the three ways by the line segments in the order you would walk, and which way do you think would be the most efficient route?

Come up with three routes you might take to do your errand and then go home. Let’s say that you want to stop at the grocery store on your way home from school.In order to write his postulates, Euclid had to describe the terms he needed and he called the descriptions “definitions.” Ultimately, we will work with theorems, which are statements that have been proved and can be proved. There were no formal geometric definitions before Euclid, and when terms could not be defined, they could be described. A postulate is another term for axiom, which is a statement that is accepted as truth without the need for proof or verification. In The Elements, Euclid summarized the geometric principles discovered earlier and created an axiomatic system, a system composed of postulates. These definitions form the foundation of the geometric theories that are applied in everyday life. In this section, we will begin our exploration of geometry by looking at the basic definitions as defined by Euclid. Determine union and intersection of sets.Express points and lines using proper notation.Identify and describe points, lines, and planes.Defining Union and Intersection of SetsĪfter completing this section, you should be able to:.

Identifying Parallel and Perpendicular Lines.

Point geometry