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Geometry Chapter 1
Study Guide
I.
Terms
A. Line: Through any two points exists exactly one line. Lines have no defined endpoints.
B. Collinear: Points on the same line
C. Plane: Through any three noncollinear points form exactly one plane.
D. Line Segment: A part of a line with two defined endpoints
E. Ray: A part of a line with one defined endpoint and an arrowhead describing the
direction of the ray.
F. Opposite Rays: Form a line
G. Midpoint: A point that divides a segment into two congruent segments.
H. Segment or Angle Bisector: A point, ray, line, line segment, or plane that intersects a
segment or angle at its midpoint.
I. Angle Types:
1. Acute Angles are less than 90˚
2. Obtuse Angles are greater than 90˚ but less than 180˚
3. Right Angles are equal to 90˚
4. Straight Angles are equal to 180˚
J. Complementary Angles: Two angles whose sum is 90˚
K. Supplementary Angles: Two angles whose sum is 180˚
L. Adjacent Angles: Two angles that share a common side
M. Linear Pair: Two adjacent supplementary angles
N. Vertical Angles: Two angles whose sides from opposite rays, vertical angles are
congruent to each other
O. Polygon: A Figure formed by three or more line segments
P. Equilateral Polygon: All sides are congruent
Q. Equiangular Polygon: All angles are congruent
R. Regular Polygon: Is both Equilateral and Equiangular
II.
Formulas and Postulates
A. Segment Addition Postulate
1. If B is between A and C, then AB + BC = AC
2. If AB + BC = AC, then B is between A and C
A
B
C
3. Examples:
a. Find XZ
X
23
Y
50
Z
b. Find GH
F
37
144
G
H
c. Find AB
36
A
-2x + 12
B
4x + 20
B. Angle Addition Postulate (Same as Segment Addition Postulate above)
C. Midpoint Formula
1.
𝑋1+𝑋2
2
(
,
𝑌1+𝑌2
)
2
2. Example 1:
Given: M is a midpoint of RS, R (1,-3) and S (4,2)
Find midpoint M
C
3. Example 2:
Given: M (8,12) is a midpoint of LP, L(-4, 2)
Find endpoint P
D. Distance Formula
1. 𝐷 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)²
2. Example:
Find the distance between R (1,-3) and S (4,2)
E. Perimeter (distance around) and Area (space inside) Formulas
Perimeter (ft)
Area (ft)2
P = 2l + 2w
A=l∙w
Square
P = 4s
A = s²
Triangle
P=b+h+s
Shape
Rectangle
Circle
Circumference = 2𝜋𝑟 𝑜𝑟 𝑑𝜋
1
A = 2 b∙h or
A = 𝜋𝑟 2
𝑏 ∙ℎ
2