Download Flowcharts

Flowcharts for most common lines of reasoning in proofs:
Prepared as of 5/7/2017 12:01 AM
Brunnlehrman
The next page consists of flowcharts.
On the left of each flowchart is the
conclusion observed (“statement”).
On the right side is the postulate,
property, or theorem (“reason”) that
explains WHY you can make the
statement.
Flowcharts for most common lines of reasoning in proofs:
Prepared as of 5/7/2017 12:01 AM
Brunnlehrman
Two Right Triangles are usually, but NOT ALWAYS, Proved Using Hyp-Leg.
𝐴𝐵 ⊥ 𝐵𝐶 𝑎𝑛𝑑 𝑋𝑌 ⊥ 𝑌𝑍
∠𝐴𝐵𝐶 𝑎𝑛𝑑 ∠𝑋𝑌𝑍 𝑎𝑟𝑒 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒𝑠
Δ𝐴𝐵𝐶 𝑎𝑛𝑑 Δ𝑋𝑌𝑍 𝑎𝑟𝑒 𝑟𝑖𝑔ℎ𝑡 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒𝑠
Given
Def of
Perpendicularity.
Definition of a Right
Triangle.
Two Right Triangles are Sometimes Proved Using Either SAS or ASA
𝐴𝐵 ⊥ 𝐵𝐶 𝑎𝑛𝑑 𝑋𝑌 ⊥ 𝑌𝑍
∠𝐴𝐵𝐶 𝑎𝑛𝑑 ∠𝑋𝑌𝑍 𝑎𝑟𝑒 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒𝑠
Δ𝐴𝐵𝐶 𝑎𝑛𝑑 Δ𝑋𝑌𝑍 𝑎𝑟𝑒 𝑟𝑖𝑔ℎ𝑡 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒𝑠
Given
Def of
Perpendicularity.
Definition of a Right
Triangle.
Flowcharts for most common lines of reasoning in proofs:
Prepared as of 5/7/2017 12:01 AM
Brunnlehrman
THE NEXT PAGE PROVIDES SOME TYPICAL QUESTIONS TO
ASK YOURSELF BEFORE WRITING THE PROOF:
(1) Is there a “bowtie?” If yes, will I need congruent vertical angles for SAS or
ASA?
(2) Are there parallel lines? If yes, will I need alternate interior angles
congruent for ASA or SAS? Corresponding angles congruent for ASA or
SAS?
(3) Is there an angle bisector? If yes, will I need congruent angles for ASA or
SAS?
(4) Is there a segment bisector? If yes, will I need congruent sides congruent for
SSS, or SAS, or ASA?
(5) Is there a perpendicular bisector? If yes, do I need congruent sides, or do I
need right angles, or both?
(6) Do the triangles share a full side so I can use Reflexive Property?
(7) Do the triangles share a full angle so I can use Reflexive Property?
(8) Do the triangles share part of a side? If yes, do I use Subtraction Property or
Addition Property?
(9) Do the triangles share part of an angle? If yes, do I use Subtraction Property
or Addition Property?
(10)
If the Givens indicate a triangle angle bisector, which angle is cut in
half?
Flowcharts for most common lines of reasoning in proofs:
Prepared as of 5/7/2017 12:01 AM
(11)
Brunnlehrman
If the Givens indicate a triangle median, which side does it cut in half?
(12)
If the Givens indicate a triangle altitude, which pair of adjacent angles
are right angles?
Some more thoughts . . .
If triangle is isosceles, then sides are congruent{ by definition}.
If sides are congruent, then opposite angles are congruent. {by theorem}