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Writing a Two-Column Proof Trivia Quiz

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?

A multiple-choice quiz by tralfaz. Estimated time: 4 mins.

Author
tralfaz

Time
4 mins

Type
Multiple Choice

Quiz #
207,695

Updated
Dec 03 21

# Qns
10

Difficulty
Average

Avg Score
6 / 10

Plays
1485

One at a Time - Single Page - Timed Game

Question 1 of 10

1. The information that is provided at the beginning of a proof is typically called the . . . Hint

free info.

givens.

starters.

beginners.

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Question 2 of 10

2. 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 . . . Hint

complements.

extras.

addenda.

supplemental.

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Question 3 of 10

3. We need to establish that in parallelogram ABCD, AB is parallel to DC and AD is parallel to BC. Our justification is . . . Hint

the definition of a parallelogram.

that we measure them.

obvious from the picture.

if they're not parallel then the answer is wrong.

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Question 4 of 10

4. In parallelogram ABCD, angle ABD is congruent to angle BDC because if we have parallel lines and a transversal, we know . . . Hint

corresponding angles are congruent.

alternate interior angles are congruent

same-side interior angles are congruent.

exterior angles are congruent.

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Question 5 of 10

5. Using the transversal BD, we can show that in parallelogram ABCD . . . Hint

AB is congruent to DC.

angle DBC is congruent to angle ADB.

angle DAB is congruent to angle BCD.

AD is congruent to BC.

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Question 6 of 10

6. We need to explicitly state that BD = BD. This idea that something is congruent to itself is called the . . . Hint

symmetric property.

substitution property.

transitive property.

reflexive property.

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Question 7 of 10

7. We have parallelogram ABCD with the diagonal BD. The Angle-Side-Angle property establishes that . . . Hint

triangle CDA is congruent to triangle BCD.

triangle CDA is congruent to triangle ABC.

triangle DAB is congruent to triangle BCD.

triangle DAB is congruent to triangle ABC.

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Question 8 of 10

8. 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 . . . Hint

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.

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Question 9 of 10

9. Three letters traditionally found at the end of a proof are . . . Hint

QEG

QEF

QED

QEE

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Question 10 of 10

10. 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 which person? Hint

Isaac Newton.

Sophie Germain.

Blaise Pascal.

Mary Somerville.

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Quiz Answer Key and Fun Facts

1. The information that is provided at the beginning of a proof is typically called the . . .

Answer: givens.

The givens form a critical part of a proof. The appearance of a diagram is not sufficient for a proof; instead all information must be explicitly given to the reader to get started.

2. 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 . . .

Answer: supplemental.

To draw a line, you MUST have two points! A common mistake I see students make is to start with one point then guess where the other end should go. That turns a construction into a sketch.

3. We need to establish that in parallelogram ABCD, AB is parallel to DC and AD is parallel to BC. Our justification is . . .

Answer: the definition of a parallelogram.

The Greek geometry teacher Euclid was the first to use the term "parallelogram". Actually, the term he used was "parallelogramic area".

4. In parallelogram ABCD, angle ABD is congruent to angle BDC because if we have parallel lines and a transversal, we know . . .

Answer: alternate interior angles are congruent

The proof of this statement is dependent upon the fact that the distance between two parallel lines is constant. Combine this with the fact that if two lines are parallel and the transversal is perpendicular to one, it is perpendicular to the other. Now it easy to make a diagram of a rectangle with a diagonal making two congruent triangles.

5. Using the transversal BD, we can show that in parallelogram ABCD . . .

Answer: angle DBC is congruent to angle ADB.

The segment BD acts as the transversal for the AB & DC combination and the AD & BC combination. To see this, you need to rotate the diagram 90 degrees.

6. We need to explicitly state that BD = BD. This idea that something is congruent to itself is called the . . .

Answer: reflexive property.

The idea that something equals itself seems very obvious but it is still necessary; it is used to determine if a relationship is an equivalence relationship. For example, 4 > 4 is not true so 'greater than' is not an equivalence relationship.

7. We have parallelogram ABCD with the diagonal BD. The Angle-Side-Angle property establishes that . . .

Answer: triangle DAB is congruent to triangle BCD.

Euclid used the phrase "similar and equal" instead of congruent. Similar means the same shape and uses the symbol ~. Equal means the same size and uses the symbol =. The symbol for congruence combines the symbols for similar and equal and is a tilde over the equals sign.

8. 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 . . .

Answer: corresponding parts of congruent triangles are congruent.

This statement is justified through superposition. If two triangles are congruent and placed on top of each other, then each side and each angle would line up perfectly as well. The idea of superposition was controversial for centuries since it is unclear if two triangles can be placed on top of each other in a plane.

The development of "rigid motions" (a.k.a. isometries) have resolved this issue.

9. Three letters traditionally found at the end of a proof are . . .

Answer: QED

for Quod Erat Demonstratum (Thus it has been shown). QEF for Quod Erat Faciendum (Thus it has been built) is used at the end of a geometric construction.

10. 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 which person?

Answer: Mary Somerville.

From Renaissance times to very recently, geometry students would buy a copy of Euclid's "Elements" and work through all thirteen books problem by problem. This created a problem for Mary Somerville in the early 1800's. Booksellers refused to sell her a copy of "Elements" because it was not thought proper for a lady to study mathematics at that time. A male friend had to buy it for her.

Source: Author tralfaz

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