Download Geometry Honors Section 1.1 Handout Getting Started

Geometry Honors
Section 1.1 Handout
Getting Started
Objectives
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Recognize, name, and create points, lines, line segments, rays, angles, and triangles
Apply the concepts of union and intersection to geometric figures
Notes
Points
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Points are represented by dots and named with capital letters
They can be thought of as being zero-dimensional
Lines
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Lines are straight and are a collection of infinite number of points
They can be thought of as being one-dimensional
They extend indefinitely in both directions
⃡ , 𝐶𝐵
⃡ , or line m
Naming lines: the line below can be named ⃡𝐴𝐵 , ⃡𝐵𝐴, ⃡𝐴𝐶 , ⃡𝐶𝐴, 𝐵𝐶
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Note how lines can be named by writing either 1) line [some lowercase letter next to the line] or
2) using two points on the line with a double arrowhead line above their letters
Line Segments
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Line segments (sometimes called simply segments) are also straight, a collection of an infinite
number of points, and are one-dimensional
Unlike lines, they have a definite beginning and end, and therefore have a finite length
The beginning and end of a segment are called endpoints
̅̅̅ or ̅𝑇𝑆
̅̅̅
Naming line segments: the line segment below can be named ̅𝑆𝑇
Rays
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Rays are also straight, a collection of an infinite number of points, and are one-dimensional
A ray is like half line and half line segment: one side of the ray is an endpoint while the other
side extends indefinitely
⃡ and 𝑍𝑋
⃡ but not 𝑌𝑍 or 𝑍𝑌
⃡
The ray below can be named 𝑋𝑌 or 𝑋𝑍 and even 𝑌𝑋
Checkpoint 1:
1. Write all of the ways you can name the following figures:
Angles
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Angles are two rays with a common endpoint. That common endpoint is the vertex of the angle.
The rays are the sides of the angle (draw a diagram below):
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The angle on the left can be named ∠𝐴𝐵𝐶, ∠𝐶𝐵𝐴, ∠1, or ∠𝐵. It cannot be named ∠𝐵𝐶𝐴 because
the vertex must be the middle letter if three letters are used. None of the angles on the right can
be named ∠𝐵 because it’s not clear whether ∠𝐴𝐵𝐶, ∠𝐶𝐵𝐷, or ∠𝐴𝐵𝐷 is being described.
Triangles
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This is a triangle. It consists of three sides which are segments and three angles. It can be called
𝛥𝐴𝐵𝐶.
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The result of a union (∪) is anything that shows up in either individual set. Thus, we can say
̅̅̅̅ ∪ ̅̅̅̅
𝛥𝐴𝐵𝐶 = ̅̅̅̅
𝐴𝐵 ∪ 𝐵𝐶
𝐴𝐶 .
The result of an intersection (∩) is anything that shows up in all individual sets. Thus, we can say
̅̅̅̅ ∩ 𝐵𝐶
̅̅̅̅ = 𝐵 because B is the only point that shows up in 𝐴𝐵
̅̅̅̅ and 𝐵𝐶
̅̅̅̅ . B (and A and C) are also
𝐴𝐵
the vertices (singular vertex) of the triangle.
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Checkpoint 2:
Determine whether each statement is always true, sometimes true, or never true.
1. The union of two rays is an angle.
2. The intersection of a line and a segment is that same segment.
Draw a diagram which matches the description.
3. ∠𝐷𝐸𝐹 ∩ 𝑅𝑆 = 𝐵
4. 𝛥𝐺𝐻𝐽 ∩ ∠𝑋𝑌𝑍 = 𝑋 ∪ 𝑊