Chapter 1 - Tools of Geometry

Intersection: Intersection of 2 or more geometric figures have common set of points. 2 lines intersect in a single point. Lines can intersect planes, and planes can intersect each other.

Undefined Terms: Terms explained using examples.

Defined Terms: Terms explained using undefined terms.

1.2

Thanks to Lekhana Chennuru

Line Segment; can be measured as it has 2 endpoints

Betweenness of Points; when there is a real number between 2 other real numbers

Congruent Segments: have the same measure

*REMEMBER CONGRUENCE DOES NOT MEAN EQUAL*

Constructions; methods of creating these figures without the benefit of measuring tools

Key Concept of Betweeness of Points (in the textbook):

Point M is between Point P and Point Q only if they all are collinear points meaning if they all lie on the same line. The equation will be PM + MQ = PQ.

Example (from textbook):

XZ = XY + YZ

XY = 3a

YZ = 14

XZ = 5a - 4

Figure out what XY is equal to.

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Explanation:

XZ = XY + YZ

3a + 14 = 5a - 4

14+4=5a-3a

18=2a

a = 9

Find XY:

XY = 3a

= 3(9)

= 27

1.3

Thanks to Ishwari Veerkar

Distance between 2 points is the length of line segment that uses those 2 points as its end points. The distance between them is the absolute value of the difference between their coordinates.

Finding Distance on Number line:
- |x1-x2| (order doesn't mater)

Finding Distance on Coordinate Plane:

1.4

Thanks to Ishwari Veerkar

Ray: Part of a line, with one end-point which extends infinitely in one direction. It is named starting with its endpoint.

Angle: Formed by 2 non-colinear rays that have common end-point.

Types of Angles:

Right Angle: 90 degrees
Acute Angle: < 90 degrees
Obtuse Angle: 90 degrees < Angle < 180 degrees
Reflex Angle: 180 degrees < Angle < 360 degrees
Straight Angle: 180 degrees
Complete Angle: 360 degrees
Angles that add up to 180 degrees: Supplementary Angles
Angles that add up to 90 degrees: Complementary Angles

Angles with same measure are called congruent angles.

Adjacent Angles: Angles next to other angle (must have these 3 things)

Common Angle
Common Side
Can't have a common interior point/ angle.

Angle Bisector: A line which bisects the angle (which makes both the angles congruent).

1.5

Thanks to Nikola Birac

Adjacent angles - two angles that have a common vertex and a common side, in the same plane

Linear pair - pair of adjacent angles with uncommon sides and opposite rays

Vertical angles - two nonadjacent angles formed by two intersecting lines

Perpendicular lines - lines that form right angles

Things you can assume - all points are coplanar

1.6

Thanks to Ishwari Veerkar

Polygon: Closed figure formed by coplanar segments called sides

Concave: A polygon whose lines when extended contain any point in the interior of the polygon

Convex: No point of the lines are in the interior of the polygon when extended

Equilateral: Same/ Congruent Sides

Equiangular: Same/ Congruent Angles

Remember: Regular polygons are equailateral as well as equiangular.

Formula for finding the sum of interior angles:

(n-2)180

Formula for finding one interior angle:

((n-2)180)/n