Blast From the Past
The Segment Within
Under Construction
hOw dO yOu kNoW tHaT?
Show me the proof
100
The criteria show in the given triangles and their relationship.
What is SSA and not congruent or similar?
100
A segment that divides and angle into two congruent parts.
What is an angle bisector?
100
The construction described in this image. 
What is the construction of an angle bisector?
100
The way of knowing for this statement: "the equations of parallel lines have the same slope because my Geometry teacher told me".
What is knowing by "authority"?
100
This can be safely assumed about the figure without the need of justification.
What is segment CE is congruent to segment CE?
200
The rotational symmetry for the given regular polygon.
What is 72 degrees?
200
A segment that intersects another segment at its midpoint and at a right angle.
What is a perpendicular bisector?
200
The construction described in this image. 
What is the construction of a parallelogram?
200
This is the Way of Knowing for the statement: "The triangles are congruent by SAS".
What is knowing something based on previously proved ideas?
200
Given the flow chart, this is the reason why there are three arrows pointing at the statement: triangle ABD is congruent to triangle CBD. 
What is AAS?
300
A series of transformations that maps figure Q onto figure R. It's very precise.
What is a translation to the right 3, followed by a reflection over the line y-axis?
300
The segment described in this image.
What is a median?
300
If we started with only segment AB, this is the first step in constructing the given figure. 
What is drawing a circle around point A with a radius of AB and a circle around B that is congruent to circle A?
300
The Way of Knowing for this statement: "The sum of the angles of a quadrilateral always add up to 360 degrees because if you draw a diagonal in it divides the quadrilateral into two triangles. Two triangles make 360 degrees.
What is knowing by "diagrams"?
300
This is the missing reason for the given proof.
What is the definition of a bisector?
400
A quadrilateral whose diagonals are perpendicular bisectors and only opposite angles are congruent.
What is a Rhombus?
400
The segment depicted in this image.
What is an altitude?
400
A reason that justifies that segments CD and CD are congruent.
What is the reflexive property?
400
A factual statement AND an example of a way of knowing by "authority".
Did you know that butterflies taste with their feed? What way of knowing is it if I say "I know this is true because I read it a book"?
400
Given that segment DB bisects angle ABC and angle A is congruent to angle C, this is a two column proof that justifies that triangle ADB is congruent to triangle CDB.
What is this..
500
A series of transformations that would map triangle YZX onto triangle TUS.
What is a translation of triangle YZX until Z maps to U and a rotation of triangle YZX around point U until YZ maps to UT.
500
A segment that intersections at the midpoints of two sides of a triangle.
What is a midsegment?
500
A reason that justifies the congruence of segments AC and AD.
What is "radii of the same circle are congruent"?
500
A factual statement AND an example of a way of knowing that fact is true by "examples".
Did you know that you can tell if a number is divisible by three if the sum of its digits are also divisible by three? What way knowing is it if I say "this is true because I tested it with the numbers 321 and 51,423.
500
Given that segment AC is congruent to angle CB and segment AC is perpendicular to BD, this proves that angle ACD is congruent to angle BCD. 
What is this?