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Geometry BasicsConcepts you must know!

How to find the distance between two points (this is the sameas finding the length of a segment).Watch this video to review how to find the distance between twopoints.

How to find the midpoint of a segmentIn order to find the midpoint of segment AC, firstfind the slope from A to C.Slope 𝑟𝑖𝑠𝑒𝑟𝑢𝑛 𝑢𝑝 2𝑟𝑖𝑔ℎ𝑡 6Since we want to find the point in the middle,divide the rise and the run by two, to find the newslope that will take you to the midpoint.Slope to find midpoint 𝑢𝑝 1𝑟𝑖𝑔ℎ𝑡 3The midpoint of 𝑨𝑪 is at (0,2).

TranslationsThis transformation could be described inthe following three ways:Using the rule (formula): 𝑥 9, 𝑦 4In words: translate the shape 9 units tothe right and 4 units down.Using translation vector 9, 4Watch video explaining this translation.

Reflection over the y axisTo reflect a point over the y axis,measure the distance from the point tothe y axis and find the point on theother side of the y axis that is locatedthat same distance from the y axis.So point C is 5 units to the right of they axis, notice that its image, C’ is 5units to the left of the y axis.Video explaining reflection over the yaxis or over the x axis

Reflection over the x axisTo reflect over the x axis, find thedistance from the point to the x axisand count that same distance on theother side of the x axis to find thelocation of the image.As you can see point B is 4 units abovethe x axis, and its image, B’ is also 4units from the x axis but under it.Video explaining reflecting over the yaxis or over the x axis.

Perpendicular bisectorWhen a point is reflected over aline, the line of reflection is theperpendicular bisector of thesegment connecting thepreimage (point P) to the image(point P’).So, 𝑃𝑀 𝑀𝑃′And right angles are formed atthe intersection.

90º CCW RotationApply the formula to each point𝑥 ,𝑦 𝑦, 𝑥The formula shows that the x value becomesthe new y, and the opposite of the y becomesthe new x value.So for example, the image of point C 4,5 is C’ 5,4Video explaining how to rotate 90 CCW

180º RotationApply the 90º rotation formula to eachpoint twice. The x value becomes the newy, and the opposite of the y becomes thenew x value.𝑥 ,𝑦2 ,5 𝑦, 𝑥 𝑥 , 𝑦 5,2 2 , 5So the image of point C 2,5 is C’ 2, 5

Angles

Linear pair anglesLinear pair angles are adjacent angles(next to each other) that together form astraight angle.These two angles are supplementary(their sum is 180º).So:𝑚 2 𝑚 1 180 Video explaining linear pair andvertical angles

Vertical anglesWhen two lines intersect, four anglesare formed.The two angles that are opposite toeach other are called vertical anglesand they measure the same.So,And 1 3 2 4Video explaining linear pair andvertical angles

Angles formed by parallel linesWhen two parallel lines are intersected by atransversal, the angles formed are equal.Although these angles have specific names,the most important fact to know is that allthe acute angles will be equal and all theobtuse angles will be equal.In the diagram you can see that all the acuteangles measure x and all the obtuse anglesmeasure 180-x.Video explaining angles formed by parallellines and a transversal

Graphing linesTo graph an equation of the form𝑦 𝑚𝑥 𝑏:1) graph the y intercept, in thisexample the y intercept is 2, soput a point at 2 on the y axis2) Find other points by using theslope, in this case you find themby going up 2, to the right 3 or bygoing down 2 and to the left 3.Video explaining how to graph 𝑦 𝑚𝑥 𝑏

Writing the equation of a lineVideo showing how to find equation of a lineIf you know a pointon a line and theslope of the line, youcan find the equationof the line by usingthe point-slopeformula.

DefinitionsPlane: a flat surfaceCollinear: points on the same lineCoplanar: points or shapes on the same planeParallel lines: two coplanar lines that never intersect.The symbol for parallel is Perpendicular lines: two lines that intersect forming right angles.The symbol for perpendicular is

Slopes of parallel, perpendicular linesIf two lines are parallel, thentheir slopes are equal.Here you can see the slope ofeach line is 2.If two lines are perpendicular,their slopes are oppositereciprocals.Here you can see the slope of one𝟐𝟑line is while the other is 𝟑𝟐

How to find the equation of a line parallelVideo showing how to find equation of parallel or perpendicular line

How to find the equation of a line perpendicularVideo showing how to find equation of parallel or perpendicular line

Shortcuts to prove two triangles arecongruent.Remember that AAA or SSA (the stinky one) cannot be used to prove that two triangles are congruent.

Triangle Angle SumExample:

Isosceles TrianglesAn isosceles triangles has twoequal sides called the legs. Theside that is not equal is called thebase.The base angles of an isosceles triangle are equal.Example:

Relationship between sides and anglesExample:Which is the smallest side in the trianglebelow?Since angle C is the smallest, the sideopposite to it would be the shortest.So the answer is side AB.

Triangle Inequality The sum of any two sides must be greater than third side orelse the three sides cannot form a triangle.

Parallelogram Properties

16.08.2011 · Geometry Basics Concepts you must know! How to find the distance between two points (this is the same as finding the length of a segment). Watch this video to review