# Geometry Survival Guide

## Big Ideas

• Triangle side measure inequalities
• Similarity transformations
• Side length proportions
• Similarity theorems (side-side-side, side-angle-side)
• Similarity postulates (angle-angle)
• Proving triangles similar with proofs
• Using midsegments and the midsegment theorem

## 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

## Big Ideas

• Theorems about parallelograms
• Theorems about quadrilaterals
• Use coordinate planes to prove or disprove a figure is a special quadrilateral
• Use coordinates to find areas and perimeters of shapes

## 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

## Big Ideas

• Proving and using the pythagorean theorem
• Set up ratios for the 6 trigonometric functions
• Use trigonomic ratios to solve right triangles
• Understand radian mesures
• Using the unit circle in the coordinate plane
• Using the unit circle to evaluate trigonometric functions

## Tips to Students

• Remember SOH-CAH-TOA: knowing this well will make it easier to solve problems quicker
• The 30-60-90 and 45-45-90 triangle rules will be helpful, so remember those
• Know how to convert radians to degrees and degrees to radians
• Know when to use the inverse of trigonometric functions

## 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

## Big Ideas

• Prove that all circles are similar
• Relationships between angles, inscribed angles, and radii
• Finding the area of a sector
• Calculate the length of an arc of a circle
• Probe properties for angles for a quadrilateral inscribed in a circle

## 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

## Big Ideas

• Finding and sketching cross sections of 3D figures
• Finding the volume of prisms with other bases
• Finding the volume of composite solids

## Tips to Students

• Remember that volume is just the area of the base multiplied by the height
• Know the formulas for the areas of different shapes
• Know the different types of 3D objects
• This unit is pretty simple - don't make it harder than it is

## 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