1. EOC Review

2. Day 1: Intro To Geometry
Starting with constructions, the most you will see on the EOC is a finished product
You need to be able to determine what is being created i.e. perpendicular bisector, ray, parallel line, etc.

3. Day 1: Intro To Geometry
Remember Conditional statement The hypothesis is the “if” the Conclusion is the “then”
If p then q
The Converse
If q then p
The Inverse
If not p then not q
The Contrapositive
If not q then not p
Note: Conditional and Contrapositive go together, Converse and Inverse go together.
If one is true the other is true if one is false the other is false

4. Day 1: Intro To Geometry Terms:
Conjecture- Something that needs to be proven; can be true and can be false
Theorem- Something that has been proven true for every case
Postulate- Something that is accepted as true without proof
Axiom- Same definition as postulate
Counterexample- An example to prove a conjecture false

5. Day 1: Intro To Geometry Acute Angle: Angle is less than 90
Obtuse Angle: Angle is more than 90
Right Angle: Angle is 90
Complimentary Angles: Angles that sum to 90
Supplementary Angles: Angles that sum to 180
Bisect: To cut in half exactly
Labeling Line, Line Segment, Angle, Ray

6. Day 1: Intro To Geometry Important Formulas from Algebra 1
Midpoint 𝑀=( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )
Distance 𝐷= ( 𝑥 2 − 𝑥 1 ) 2 + ( 𝑦 2 − 𝑦 1 ) 2
Point-Slope y− 𝑦 1 =𝑚(𝑥− 𝑥 1 )
Slope Intercept 𝑦=𝑚𝑥+𝑏
Slope 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1

7. Day 2: Transformations and Intro to Triangles
First Concave & Convex
Convex- No angles are greater than 180 in a polygon
Concave- 1 or more angles are greater than 180
Vertical Angles Theorem
<1≅ <3 𝑎𝑛𝑑 <2≅ <4

8. Day 2: Transformations and Intro to Triangles
Remember Parallel and Perpendicular
Parallel Lines never cross and when their slopes are the same
Perpendicular lines intersect and form 90˚ angles, the product of their slopes is -1
Ex: are the lines y=5x+4 and 5y=-25x+5 perpendicular or parallel or neither?

9. Day 2: Transformations and Intro to Triangles
A transformation is a change in position, size or shape of a figure on a plane
Pre-ImageBefore
Image After
Rigid Motion- Preserves the size and shape of the figure
Translation- Rigid Motion where all the points are moved equal distance
Rotation- Rigid Motion and a turn about the center of rotation Labeled as 𝑟 (𝑥∘, 0,0 )
Reflection- Rigid Motion and a flip over a line of reflection
See image for notation

10. Day 2: Transformations and Intro to Triangles
Symmetry is a rigid motion that maps the figure onto itself
There are different types of symmetry
Reflection Symmetry- This occurs when the reflection is the exact same image
Rotational Symmetry- This occurs when the image rotates less than 360 degrees and maps onto itself
Point Symmetry- This occurs when a 180 degree rotation about a center of rotation maps the figure onto itself

11. Day 2: Transformations and Intro to Triangles
Non Rigid Motion- A transformation that changes the size or shape of an object
A dilation is a transformation that changes the size of a figure. It can become larger or smaller, but the shape of the figure does not change. Knowing the scale factor allows you to predict what the image will look like after the dilation
If the Center or point of Dilation is at the origin (0,0) then apply the scale factor to the coordinates
EX: Dilate the ponts A(0,1), B(3,5), C(5,2) by a scale factor of 3. The center of dilation is (0,0)

12. Day 2: Transformations and Intro to Triangles
Triangles- A closed figure with 3 sides and angles
Many different types
First with regards to their angles
Right- One right angle in the triangle
Obtuse- one angle that measures greater than 90
Acute- All angles are less than 90
Next with regards to their sides
Equilateral- all sides are equal
Scalene- no sides are equal
Isosceles- two sides are equal

13. Day 3: Triangles and their Theorems
A lot of theorems you need to know
Triangle Midsegment Theorem- The Midsegment divides the triangle sides in half
Triangle Sum Theorem- All angles in a triangle add to 180
Triangle Proportionality Theorem- If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.
Triangle Inequality Theorem- The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Triangle Exterior Angle Theorem- exterior angle of a triangle is greater than either of the measures of the remote interior angles l

14. Day 3: Triangles and their Theorems

15. Day 3: Triangles and their Theorems
Congruent Triangle Theorems
SSS- Side Side Side Postulate
3 Sides are congruent to each other
SAS- Side Angle Side Postulate
2 sides are congruent and the angle in between the sides is congruent
ASA- Angle Side Angle Postulate
2 angles are congruent and the side between them is congruent
AAS- Angle Angle Side Theorem
Two consecutive angles are congruent and the opposite side is congruent also
SSA- Side Side Angle Theorem
Two consecutive sides are congruent and the opposite angle is also congruent
HL- Hypotenuse-Leg Theorem
The triangle has a right angle, hypotenuse, and a leg congruent to another triangle

16. Day 3: Triangles and their Theorems
Similar Triangle Theorems

17. Day 4: Lines and Transversals
Corresponding Angles- one inside and outside the parallel lines, same side of transversals
<1 and <5
Alternate Interior Angles- Both are inside the parallel lines and on opposite sides of the transversal
<3 and <6
Alternate Exterior Angles- Both are outside the parallel lines and on opposite sides of the transversal
<1 and <8
Same-Side Interior Angles- Both are inside the parallel lines and on the same side of the transversal
<4 and <6

18. Day 5: Special Right Triangles
In any right triangle the Pythagorean Theorem is true
𝑎 2 + 𝑏 2 = 𝑐 2 , where c is the Hypotenuse and a/b are the legs
The converse is equally as important
The Converse of the Pythagorean Theorem is just flipped around
It says if 𝑎 2 + 𝑏 2 = 𝑐 2 then the triangle is Right
This also leads us to two other theorems
If 𝑎 2 + 𝑏 2 > 𝑐 2 then the triangle is Acute
If 𝑎 2 + 𝑏 2 < 𝑐 2 then the triangle is Obtuse

19. Day 5: Special Right Triangles
Now to our Special Right triangles. There are two types
This is an isosceles right triangles
This is a scalene right triangle

20. Day 5: Special Right Triangles
On to Trigonometry!
Remember SOH CAH TOA
Sine= Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent= Opposite/ Adjacent
Cosecant= Hypotenuse/ Opposite
Secant= Hypotenuse/ Adjacent
Cotangent= Adjacent/ Opposite

21. Day 6: Quadrilaterals and Proofs
There are a number of important properties of quadrilaterals
Parallelograms
Opposite sides are congruent and parallel
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals Bisect each other
In a Rhombus
All properties of parallelograms apply
All sides are congruent
Diagonals are perpendicular
In a Rectangle
All properties of a parallelogram apply
All angles are Right Angles
Diagonals are congruent
In a Square
All properties of Rectangles and Rhombuses apply
All sides are equal and all angles are right angles

22. Day 6: Quadrilaterals and Proofs
Trapezoid
A quadrilateral with one pair of parallel sides
Isosceles Trapezoid
A Trapezoid with one pair of congruent sides and one pair of parallel sides
Base Angles are congruent
The diagonals are congruent
The Midsegment is equal to 1 2 ( 𝑏 1 + 𝑏 2 )
Kite
A quadrilateral with two pairs of congruent sides that are consecutive
Diagonals are perpendicular

23. Day 6: Quadrilaterals and Proofs

24. Day 6: Quadrilaterals and Proofs
Angle Sum Theorem
Opposite Sides in Parallelogram

25. Day 7: Polygons and their formulas
Polygon- A closed geometric figure with sides formed by 3 or more coplanar segments at each endpoint
Interior Angles– Angles inside a polygon
𝑛−2 ∗180 This is for the total measure
𝑛−2 ∗180 𝑛 This is for a single angle in a regular polygon
Exterior Angles– Angles outside the polygon
All exterior angles sum to 360˚
To find a single angle in a regular polygon: 360 𝑛

26. Day 7: Polygons and their formulas

27. Day 7: Polygons and their formulas
Perimeter- Remember to add all the sides for this
Area Formulas
All polygons can use Area= 1 2 𝑎𝑃
We will use this with area of Pentagons, hexagons, octagons, etc.
Triangles
Area= 1 2 𝑏ℎ
Parallelograms
Area=bh
Area=𝑙𝑤
Trapezoids
Area= 1 2 ( 𝑏 1 + 𝑏 2 )h

28. Day 8: Circles

29. Day 8: Circles Important things to remember about arcs and sectors
Arc measure is equal to the central angle
You can calculate arc length and Circumference
𝐴𝑟𝑐 𝐿𝑒𝑛𝑔𝑡ℎ= 𝜃 360 ∗2𝜋𝑟
C=2𝜋𝑟
You can calculate sectors and area
𝐴=𝜋 𝑟 2
Sector= 𝜃 360 ∗𝜋 𝑟 2
Remember Radian Measure= 𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑟𝑎𝑑𝑖𝑢𝑠
To convert Degrees to radians
𝜋 180
To convert Radians to degrees
180 𝜋

30. Day 8: Circles Remember the equation of a circle
(𝑥−ℎ) 2 + (𝑦−𝑘) 2 = 𝑟 2
Where (h,k) is the center of the circle and r is the radius
Remember to flip the sign of h and k!
You may be required to complete the square

31. Day 8: Circles
Inscribed Angle- An angle inside a circle whose vertex is on the circle
Intercepted Arc- an arc who is inside the chords of the inscribed angle
The measure of an inscribed angle is HALF the intercepted arc measure
If a quadrilateral is inscribed a circle the opposite angles are supplementary
A tangent is a line that intersects the circle at 1 point
Tangents are perpendicular to the radius
A chord and tangents angle is half the intercepted arc

32. Day 8: Circles

33. Day 8: Circles

34. Day 8: Circles

35. Day 9: 3D and Modeling
First remember

36. Day 9: 3D and Modeling
Volumes and Surface Area Formulas

37. Day 9: 3D and Modeling Pyramid Volume Pyramid Surface Area
1/3(lwh) if quadrilateral base
1/3(1/2bh) if triangular base
Pyramid Surface Area
1/2Ps+ bh, where P is perimeter and s is slant height: Square base
1/2Ps+ 1/2bh if triangle base

38. Day 9: 3D and Modeling Remember Similar Solids! IXL T.8
If you have a scale factor length and you need to find:
Volume Cube it!
Surface Area Square it!
Cavaleri’s Principle
Density= 𝑂𝑏𝑗𝑒𝑐𝑡 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡