THE COMPOUND // FIELD NOTES // WEEK 01
Geometry review, polygons, and exponent theorems
Method
Paper first, every step
The Compound opens its books on day one. This week restores the geometry facts the whole year leans on, then puts the exponent theorems on the record.
What you have to be able to do
- Name angle pairs and use their sums
- Find perimeter, area, and volume of the basic figures
- Apply the product and power theorems for exponents
The procedures
Angle factsField Book Lesson A
- Acute is less than 90, right is exactly 90, obtuse is between 90 and 180, straight is 180.
- Complementary angles sum to 90. Supplementary angles sum to 180.
- When two lines cross, vertical angles are equal.
Perimeter, area, volumeField Book Lesson B
- Perimeter: add every side. The only formulas are for circles and semicircles.
- Area: rectangle is bh, triangle is 12bh, circle is πr2.
- Volume of a right solid: area of the face times the depth.
Polygons and trianglesField Book Lesson 1
- Classify a polygon by its number of sides.
- The three angles of any triangle sum to 180.
- A transversal across parallel lines makes equal alternate angles.
Exponent theoremsField Book Lesson 2
- A negative exponent moves the factor: x-n means 1xn.
- Product theorem: xaxb = xa+b.
- Power theorem: (xa)b = xab.
Worked: a supplementary pair
- Two supplementary angles measure x and x + 40.
- x + x + 40 = 180
- 2x = 140, so x = 70. The angles are 70 and 110.
Terms on the record
| Term | Meaning |
|---|
| acute angle | an angle measuring less than 90° |
| supplementary angles | two angles whose measures sum to 180° |
| product theorem | to multiply powers of the same base, add the exponents |