Proofs
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Card preview (15)
Reflexive axiom
Figure is equal to itself x=x
Symmetric axiom
Switch left side of equation to right side y+x=x+y
Addition/Subtraction axiom
You can add/subtract same figure to/from both sides of equation (if 3x-2 =4, then 3x =)6
Multiplication/Division axioms
You can multiply/divide both sides of equation by same factor/scale
Substitution axiom
Numbers equal to each other can be substituted
Segment/angle addition
Part + part = whole
Linear pairs are…
Supplementary
Supplements of congruent angles are…
Also congruent
What do perpendicular lines form?
Right angles
Vertical lines are…
Congruent
All right angles are…
Congruent
Median of triangle
Line segment drawn from vertex of triangle to MIDPOINT on opposite side (no proof they are right angles but they are congruent to each other)
Altitude of a triangle
Line segment drawn from the vertex of the angle so it is perpendicular to the other side (no proof there was a midpoint but they are RIGHT TRIANGLES)
Subtraction & Addition proof strategy
Given (Reflexive) segment/angle addition/subtraction, substitution, addition/subtraction axiom at end
Division proofs
Given, definition of midpoint/bisector, angle/segment addition axiom, substitution (to make each part equal), substitution (to make both factors the same on both side), division axiom