Presentation On Theme: Holt Geometry 3
1 Holt Geometry 3-1 Lines and Angles
2 Holt Geometry 3-1 Lines and Angles Example 2: Classifying Pairs of Angles Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles 1 and 5 D. same-side interior angles 3 and 5 1 and 7 3 and 6
3 Holt Geometry 3-1 Lines and Angles Check It Out! Example 2 Give an example of each angle pair. A. corresponding angles B. alternate interior angles C. alternate exterior angles 1 and 3 D. same-side interior angles 2 and 7 1 and 8 2 and 3
Definition Of A Line Segment
A line segment is a segment of a line, or in other words, we can say that a line segment is a line with two endpoints.
For example, The diagram shows a line L and one segment of this line is AB.
In a plane, there can be many lines or line segments.
And, these lines can be divided into a few types based on the relative positioning of a line with another line.
Lines And Angles Definitions Properties Types Practice Questions
Ancient mathematicians introduced the concept of lines to represent straight objects which had negligible width and depth. Considered as a breadth less length by Euclid, lines form the basis of Euclidean geometry.
When two rays intersect each other in the same plane, they form an angle. The point of intersection is called a vertex.
In this article, we go over the basic properties, definitions, and types of lines and angles related to geometry. Well also look at a few examples for you to understand the properties of lines and angles in a better manner. Before we move forward, take a look at the five-step GMAT Preparation plan to score 700+ on the GMAT:
A line does not have any endpoints. It has an infinite length.
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What 7 Concepts Are Covered In The Consecutive Interior Angles Calculator
- consecutive interior angles
- the pairs of angles that are between two lines and on the same side of the line cutting through the two lines.
- interior angles
- the angles between adjacent sides of a rectilinear figure
- parallel lines
- two lines which never cross and always the same distance apart
- proof
- an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion
- supplementary angles
- Two angles are supplementary angles if the sum of their measures is equal to 180°
- transversal
- a line that passes through two lines in the same plane at two distinct points.
- two column proof
- This consists of a list of statements, and the reasons that we know those statements are true. The two column proof has five parts:1) Given
Angles Formed By A Transversal Line
When a transversal line intersects two lines, then eight angles are formed as shown.
Now, there are several special pairs of angles that are obtained from this diagram.
For example: If you notice , , , and are all vertically opposite angles.
Similarly, we get several other types of angles. Let us discuss them.
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Sum Of Angles Around A Point
The sum of all the angles around a point is always 360 degrees.
For example, Sum of angles around point O is 360 degrees.
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Step 3: Approach and Working out
To find Y-X, we need to find Y and X first.
Measure of angle Y:
- We are given AFC = 100° and,
- AFC + BFC = 180° as the sum of angles on the same side straight line is 180°
- 100° + BFC = 180°
Measure of angle X:
- We are given BFE = 45° and,
- DFE + BFE + BFC = 180° as the sum of angles on the same side straight line is 180°.
- X + 45° +80°= 180°
Hence, Y X = 80° 55° =25°.
Thus, the correct answer is option B.
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