Formulas for Geometry, Study notes of Geometry

Formulas and definitions related to geometry, including the segment addition postulate, distance formula, midpoint formula, partitioning ratio, slope formulas, and properties of parallelograms. It also includes examples and diagrams to illustrate these concepts. The document could be useful for students studying geometry who need a quick reference for formulas and definitions.

Typology: Study notes

2022/2023

Available from 03/25/2023

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221 Geometry
Brunswick High School
Midterm Exam Formula
Geometry Midterm Exam Formula
Segment Addition Postulate: Little + Little = Big (LM + MO = LO)
The pink lines represent that both segments LM and MO are congruent or equal. Both segment LM
and MO added together will equal the whole segment LO.
Distance Formula: (xโ‚ , yโ‚) (xโ‚‚ , yโ‚‚)
๐‘‘= (๐‘ฅโ‚‚ , ๐‘ฅโ‚)2+(๐‘ฆโ‚‚ , ๐‘ฆโ‚)2
The distance formula can be used to ๏ฌnd the distance between two coordinates on a coordinate
plane.
Midpoint Formula:
2โ€ข (๐‘ฅโ‚+ ๐‘ฅโ‚‚)
2, 2โ€ข (๐‘ฆโ‚+ ๐‘ฆโ‚‚)
2
The midpoint formula is used to ๏ฌnd the middle point of two end coordinates. For example, ๏ฌnding
the midpoint of point a and point b.
Partitioning Ratio: 1 : 2 โ†’ ๐‘Ž
๐‘โ†’๐‘Ž
๐‘Ž+๐‘ โ†’ 1
3
๐‘ฅ=๐‘ฆ+๐‘š (๐‘ฅโˆ’๐‘ฆ)
๐‘ฆ=๐‘ฆ+๐‘š (๐‘ฅโˆ’๐‘ฆ)
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221 Geometry Brunswick High School Midterm Exam Formula

Geometry Midterm Exam Formula

Segment Addition Postulate: Little + Little = Big (LM + MO = LO) The pink lines represent that both segments LM and MO are congruent or equal. Both segment LM and MO added together will equal the whole segment LO. Distance Formula: (xโ‚ , yโ‚) (xโ‚‚ , yโ‚‚) ๐‘‘ = (๐‘ฅโ‚‚ , ๐‘ฅโ‚) 2

  • (๐‘ฆโ‚‚ , ๐‘ฆโ‚) 2 The distance formula can be used to find the distance between two coordinates on a coordinate plane. Midpoint Formula: 2 โ€ข (๐‘ฅโ‚+ ๐‘ฅโ‚‚) 2

(๐‘ฆโ‚+ ๐‘ฆโ‚‚) 2 The midpoint formula is used to find the middle point of two end coordinates. For example, finding the midpoint of point a and point b. Partitioning Ratio: 1 : 2 โ†’ ๐‘Ž ๐‘

๐‘Ž ๐‘Ž+๐‘

1 3 ๐‘ฅ = ๐‘ฆ + ๐‘š (๐‘ฅ โˆ’ ๐‘ฆ) ๐‘ฆ = ๐‘ฆ + ๐‘š (๐‘ฅ โˆ’ ๐‘ฆ)

The partitioning ratio is to find the midpoint too. You can use this formula when you want to find the midpoint of a number line. Parallel: same slopes Perpendicular: opposite reciprocal slopes for example ๐‘ฆ = โˆ’ 2๐‘ฅ the opps. reciprocal slope is๐‘ฆ = 1 2

Slope Formulas :

  1. ๐‘ฆ = ๐‘š๐‘ฅ + ๐‘ โ†’Slope equation
  2. ๐‘ฆ โˆ’ ๐‘ฆโ‚ = ๐‘š(๐‘ฅโ‚ โˆ’ ๐‘ฅ) โ†’Slope Intercept form
  3. ๐‘š = Finding the Slope ๐‘ฆโ‚‚โˆ’ ๐‘ฆโ‚ ๐‘ฅโ‚‚โˆ’๐‘ฅโ‚

Interior Angle sum: (๐‘› โˆ’ 2) * 180 โ†’ ๐‘› = ๐‘ ๐‘–๐‘‘๐‘’๐‘  Exterior Angle sum: 360 degrees Finding the amount of sides: ____ยฐ๐‘› = (๐‘› โˆ’ 2) * 180

Properties of Parallelogram

Definition: If ABCD is a parallelogram, then โ€ฆ Definition Picture How it looks in proof