Geometry by Gael Olvera

Foundation of Geometry

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Point - Location, no shape, no size, EX : Point A

Line - 2 points, no width or height, infinite, EX : Line XY

Plane - Blank surface, 3> points, EX : Plane KJL

Collinear - Points that lie on the same line

Coplanar - Points that lie on the same plane

Intersect - Lines or planes making contact

Distance Formula - √ (x₂ - x₁)² + (y₂ - y₁)²

Midpoint Formula - (x₁ + x₂)/2, (y₁ + y₂)/2.

Conditional Statements and Venn Diagram

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If > Then, Hypothesis > Conclusion

EX : If you live in Nashville then you live in Tennessee

Inverse - ~P > ~Q

Converse - Q > P

Contrapositive - ~Q > ~P

If it is Saturday, then there's no school

Inverse - If it's not Saturday, then there's no school F

Converse - If there's no school, then it's Saturday F

Contrapositive - If there is school, then it's not Saturday T

Biconditional Statements - (P>Q) ^ (A>P)

P > Q - Circle inside circle

P down Q disjunction - both circles and middle shaded

P ^ P conjunction - middle shaded

Parallel and Perpendicular Lines

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Parallel - Lines that never cross

Perpendicular - Opposite Reciprocals

EX : 3/4, 3/4, / 2/5, -5/2

(X2 -X1) , (Y2- Y1)

Point Slope and Standard Form

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Point Slope - (Y2 - Y1) = M(X2 - X1)

EX : (4, 1) Slope = 2

Y - 1 = 2(X - 4)

Standard - Ax + By = C

Slope Intercept - Y = mx + b

EX : 5X + 2Y = -2

Y = -5/2x - 1

EX : 2X - 4Y = 28

Y = 1/2X - 7

Triangle Congruence: SSS, SAS, ASA, AAS, HL

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SSS - 3 pair congruent sides

SAS - Two sides and angle

ASA - Two angles and slide

AAS - Two angles and side opposite are congruent

HL - Right angle

Congruent Sides - Given, Def of midpoint, Reflexive property

Congruent Angles - Given, Vertical angles, alt interior, Corresponding angles, Def of angle bisector

Parallelograms

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Parallelograms - 4 sides 2 parallel lines, Opposite sides/angles congruent, Consecutive angles supplementary (180), Diagonals bisect each other

Rectangles

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Rectangles - Opposite sides are congruent, Parallel, Congruent, Consecutive angles are supplementary, Diagonals bisect each other, All 4 angles are right 90, Diagonals are congruent

Rhombi

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Rhombi - Opposite sides congruent and parallel, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, 4 sides congruent, Diagonals perpendicular, Diagonals bisect opposite angles

Squares

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Squares - Opposite sides are congruent/parallel, opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, Four right angles, Diagonals are congruent, Four congruent sides, Diagonals are perpendicular, Diagonals bisect opposite angles

Trapezoids

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Non-isosceles Trapezoids - Only one pair of opposite sides are parallel, Consecutive angles between parallel lines are supplementary

Isosceles Trapezoids - Non-parallel sides are congruent, Diagonals are congruent, Base angles are congruent, Opposite angles are supplementary

Midsegment of a trapezoid

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X - Midsegment of triangle x2 = Both upper and lower leg combined

EX : If AB = 14 and DC = 26, find EF

EF = 14+26/2

EF = 20

EX : If EF = 22 and DC = 38, find AB

22x2 = AB + 38x2

44 = AB + 38

AB = 6

Kites

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Kite - Exactly two pairs of consecutive congruent sides (AB = AD and BC = DC), One pair of opposite angles are congruent (ABC = ADC), Diagonals are perpendicular (AC T BD)

Credit

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1 - https://www.flickr.com/photos/internetarchivebookimages/14779059731/

2 - https://en.wikiversity.org/wiki/File:Venn_Diagram_(P,Q).jpg

3 - https://commons.wikimedia.org/wiki/File:Slopes_of_Parallel_and_Perpendicular_Lines.svg

4 - https://commons.wikimedia.org/wiki/File:Y-intercept_line_gen_m.svg

5 - https://commons.wikimedia.org/wiki/File:Angle-angle-side_triangle_congruence.svg

6 -https://commons.wikimedia.org/wiki/File:Parallelogram_simple.svg

7 -https://commons.wikimedia.org/wiki/File:Rectangle_Geometry_Vector.svg

8- https://commons.wikimedia.org/wiki/File:Polyhedron_great_rhombi_6-8_subsolid_snub_right.png

9- https://commons.wikimedia.org/wiki/File:Square_wave.svg

10 - https://commons.wikimedia.org/wiki/File:Trapezoid,_area_problem,_square_units.png

11- https://upload.wikimedia.org/wikipedia/commons/6/67/%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D1%8F%D1%8F_%D0%BB%D0%B8%D0%BD%D0%B8%D1%8F_%D1%82%D1%80%D0%B0%D0%BF%D0%B5%D1%86%D0%B8%D0%B8.png

12- https://www.flickr.com/photos/64320116@N08/15865950498