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-Undefined terms help define other terms in geometry like point, line, and plane. Point is has no dimension and is represented by a dot. Line has a one straight dimension, made of infinitely points, and extends in two directions. Plane has two dimensions, represented by a shape that looks like a floor, and extends infinitely.

-Distance formula: d=√((x_2-x_1)²+(y_2-y_1)²)

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

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Conditional Statements and Venn Diagrams

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Conditional Statements and Venn Diagrams

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-Conditional Statements are written in if-then form. The hypothesis would be the phrase that follows IF, and the conclusion would be the phrase that follows THEN. For example, IF a quadrilateral is a square, THEN it has four right angles. The hypothesis would be that a quadrialteral is a square, and the conclusion would be that it has four right angles.

-Venn Diagrams help to show relationships between two things. For example, if the circle is inside the other circle, this means that all of those elements are part of the same elements. When the circles interconnect, then it means that only some elements are the same. However, if they have no touch, it means there is no relationship between them.

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-Point Slope: y-y₁=m(x-x₁)

Point slope would look like the example above which would be y-5= 3(x-4). However, if it's not given what you would do is grab the y from the first coordinates, plug in the slope, and then put in the x of the same coordiantes as the previous one.

-Standard Form: Ax+By=C

To get standard form you would make your equation be inverse. For example, if you have 2y=-5x + 7, you are going to try to put it in the order of the formula. -5x would become postive as it moves next to 2y. The final product woud be -5x + 2y=7

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-Parallel lines are two coplanar lines that never intersect. The symbol: ll is used to indicate the lines are parallel.

-Perpendicular lines intersect each other.

EX: line f(x)= 2x + 3 and line j(x)= 2x-6 are parallel to each other since they don't touch.

EX: here one of the lines that intersect each other would be line h(x)= -2x + 2 and f(x)= 2x + 3, making it perpendicular.

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

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

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SSS: Three pairs of equal sides.

SAS: Two sides and an angle is congruent.

ASA: Two angles and a given side are congruet.

AAS: Two angles and a side opposite them are congruent.

HL: (Hypotenuse-Leg) The hypotenuse and any one leg of a right triangle are equal.

Congruent Sides: given,defenition of midpoint(creates two equal sides), and reflexive property( a side congruent to itself).

Congruent Angles: given, vertical angles, alternate interior angles, coressponding angles; those two must be parallel lines, and defenition of angle bisector which will create two congruent angles.

EX: When looking at a problem you should start by looking at the givens, there it would be easier to detect the ones you have to find. To know for sure when they have alterante interior angles or coressponding angles make sure there is an actual angle.

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A paralleogram is a quadrilateral in which both pairs of opposite sides are parallel.

Properties of paralleograms: opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, and diagonals bisect each other.

EX: BC ll AD this means that you would set up your equation as 4x-10=3x+5 which would give you x=15. If you plug it in each one would be 50. These steps were used out of the properties if facing an even more difficult question the best thing to use is the main properties.

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Rectangles have the same properties as parallelograms plus these: all four angles are right angles and diagonals are congruent.

EX: in this problem if your trying to find DC the thing you could do is set up your equation as 3x + 1= 3x+1 since your trying to find the other segments and those two are equal to eachother. For final result you would get x=1. Here then you would plug it in so 3(1)+1=4 DC would equal to 4. This is just one way to find a segment but there is many different problems and with angles as well.

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Rhombi have the same properties as parallelograms but they have the following 3: all 4 sides are congruent, diagonals are perpendicular, and diagonals bisect opposite angles.

EX: when you have a rhombi and they give you givens such as; JK=12 and JN=7, and they are asking you to find JM and JL. The first thing you would do is look at the rules and then you will notice that JM= 12. Next, to find JL you will add segment JN and NL together wich both are 7 and will equal to 14, so the whole segment would be 14.

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A square has all the properties of a paralleogram, rectangle, and rhombus.

EX: if a square is given, and is asking you to find X you will do the following steps. Imagine one of the angles given is 7x+3, so the set up of your equation would be 7x+3=45, the reason it's 45 is because it is half of 90 and it's only asking you one part of the angel. The final result would be x=6.

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Non-Isosceles Trapezoids properties are: only 1 pair of opposite sides are ll and consecutive angles between ll lines are supplementary.

Isosceles Trapezoids: have the same properties as the ones above plus non-parallel sides are congruent, diagonals are congruent base angles are congruent, and opposite angles are supplementary.

EX: When looking for a missing side, you will get the given side and subtarct it by 180. Lets say A is 87 and you want to find B, you will get 180-87 and have a result of 93.

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Midsegment of a trapezoid connects the midpoints of the legs: AB ll CD ll EF and EF= segement AB + segment CD/ 2.

EX: AB is 38, SR is x + 14, and YZ which is the midpoint is 5x-19. The equation would be set up as 5x - 19 = x + 4 + 38 / 2, here 5x-19 would be multiplied by 2. Your answer would be 10x + - 38 = x + 52 then you would do the steps and get X= 10 as the final answer, and YZ would be 31.

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Kites have the following properties: exactly 2 pairs of consecutive congruent sides, one pair of opposite angles are congruent, and diagonals are perpendicular.

EX: a problem is asking for angle B and D and the ones given are A=85 and C=43. The step you'll have to do is subtract 360-85-43/2 which gives you 116. B would be 116 and also D since they are opposite angles.

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Slide 1: https://www.geogebra.org/m/bsrkz3en

Slide 2:

https://www.teacherspayteachers.com/Product/Venn-Diagram-Examples-for-Conditional-Statements-Notes-Handout-4748203

Slide 3: https://courses.lumenlearning.com/waymakercollegealgebra/chapter/parallel-and-perpendicular-lines-2/

Slide 4: https://www.youtube.com/watch?v=AxKx3jrjXFA

Slide 5: https://www.onlinemathlearning.com/prove-triangles-congruent.html

slide 6:https://www.basic-mathematics.com/properties-of-a-parallelogram.html

slide 7: https://allthingsmathematics.wordpress.com/2014/03/13/geometry-9th-grade-practice-problems/

Slide 8: https://www.slideshare.net/slideshow/5-lesson-3-rectangles-rhombi-and-squares/76751678

Slide 9: https://en.wikibooks.org/wiki/Geometry_Course/Polygon/Quadrilateral/Square

Slide 10:https://mathmonks.com/trapezoid

slide 11:https://andymath.com/trapezoid-midsegment/\

slide 12:https://mathmonks.com/kite

slide 13: https://www.greatspecials.shop/?ggcid=1903903