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Writing a Two-Column Proof
"Two-column proofs are the bane of a geometry student's existence. Draw a parallelogram and label the corners ABCD going clockwise. We are going to prove that the opposite sides are congruent. Ready to go?"
15 Points Per Correct Answer - No time limit
The information that is provided at the beginning of a proof is typically called the . . .
The first thing we do is to draw a segment from B to D. Items added to a geometric diagram to help with the proof are called . . .
We need to establish that in parallelogram ABCD, AB is parallel to DC and AD is parallel to BC. Our justification is . . .
the definition of a parallelogram.
that we measure them.
obvious from the picture.
if they're not parallel then the answer is wrong.
In parallelogram ABCD, angle ABD is congruent to angle BDC because if we have parallel lines and a transversal, we know . . .
corresponding angles are congruent.
exterior angles are congruent.
same-side interior angles are congruent.
alternate interior angles are congruent
Using the transversal BD, we can show that in parallelogram ABCD . . .
AB is congruent to DC.
AD is congruent to BC.
angle DAB is congruent to angle BCD.
angle DBC is congruent to angle ADB.
We need to explicitly state that BD = BD. This idea that something is congruent to itself is called the . . .
We have parallelogram ABCD with the diagonal BD. The Angle-Side-Angle property establishes that . . .
triangle CDA is congruent to triangle ABC.
triangle CDA is congruent to triangle BCD.
triangle DAB is congruent to triangle ABC.
triangle DAB is congruent to triangle BCD.
We have parallelogram ABCD with the diagonal BD. We write AB is congruent to DC and AD is congruent to BC. Our last justification is . . .
the area of a triangle is bh/2.
all three sides of an equilateral triangle are congruent.
corresponding parts of congruent triangles are congruent.
if two angles of a triangle are congruent, the triangle is isosceles.
Three letters traditionally found at the end of a proof are . . .
This proof can be found in Euclid's "Element" as Book I, Proposition 34. There is a famous story that a book seller refused to sell a copy of "Elements" to . . .
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Compiled Jun 28 12