# Geometry Survival Guide

### Alicia Kuester

## Triangles and Similarity - Unit 6

## Tips to Students

- A triangle cannot be constructed from three line segments if any of them is longer than the sum of the other two
- In similar polygons, the corresponding angles must be congruent and the ratios of pairs of corresponding sides must all be equal
- Always mark your diagrams! It is easier to solve the problem when you know exactly what numbers you are working with
- Triangles are similar if two pairs of angles are congruent (3rd angles theorem)
- Remember the midsegment theorem! It is a very useful theorem when you are working with triangles
- A line parallel to one side of a triangles divides the other two proportionally

## Things I Struggled With

- Figuring out possible side lengths - I just remembered to add the two shortest sides and that sum is the biggest the longest side length can be, and subtract the two given side lengths and that is the shortest the unknown side length can be
- Proving polygons similar - I learned this by remembering the rules for each polygon, so it would be easier to show that two are similar
- Remembering the triangle theorems and postulates (side-side-side, side-angle-side, angle-angle) - it was easier to remember the letters (SSS, SAS, AA) and then I learned those from the letters

## Quadrilaterals - Unit 7

## Tips to Students

- Remembering the rules and properties of the quadrilaterals will make this unit a lot easier
- When finding angle measures, just remember that all polygons have angles that add up to 360 degrees
- Memorizing the formula for slope and the distance formula will make it easier to prove quadrilaterals in a coordinate plane
- Remember all of the ways to prove quadrilaterals in a coordinate plane, it will make it easier when you have to show your work and explain how you did what you did

## Things I Struggled With

- Remembering all of the properties for each quadrilateral - to learn this I kept reading them and practicing using them with different shapes
- Knowing how to prove what a quadrilateral is in a coordinate plane - to learn the rules for each quadrilateral I had to practice with each multiple times, and then I remembered how to prove each shape

## Trigonometry - Unit 8

## Things I Struggled With

- Remembering the difference between angle of depression and angle of elevation - if the person/thing is looking up at something it is angle of elevation, and if it is looking down then it is angle of depression
- Reading the unit circle - it looks hard at frist, but once you write everything in and practice using it, it gets easier to use
- Knowing when to use the trigonometric functions and their inverse - to figure out what functions to use, I always write in the hypotenuse, opposite, and adjacent on the sides of the triangles, inverse functions are used when you are finding an angle measure instead of a side length

## Circles - Unit 9

## Tips to Students

- Remember the vocabulary for circles - it is easy to get the wrong answer if you are looking for the wrong thing
- Remember area and circumference formulas for circles
- Remember that all circles are similar
- A tangent line and radius are always perpendicular
- Remember the rules for angle relationships within circles

## Things I Struggled With

- Knowing the angle relationships within circles
- Finding the area of a sector - I remembered to use the area formula, and to use the angle measure/360
- Remembering the formulas for area and circumference of a circle - I remembered that r^2 is in the area formula so then I automatically knew that 2pi r is the circumference formula

## Volume - Unit 10

## Things I Struggled With

- Knowing how to find the volume of a hexagonal prism - I remembered that volume is just the area of the base multiplied by the height, so I had to find the area of the hexagon first
- Finding cross sections in 3D figures - I pictured the figure as if it was a specific 3D object (a cylinder as a can) and then saw in my head as if I were cutting a section out of it