Compare geometry
Compare two quantities using the given information. Then change the geometry to explore why the relationship holds.
Reason from triangle sums, parallel lines, and exterior angles.
Triangle sums
1 comparison · No time limit · Explore after checking
Example
Example
Compare the sum of the two unknown angles with Quantity B.
Review the comparison
One interior angle of the triangle is 80°.
The other two interior angles are x and y.
One possible triangle. Use the stated angle, not the drawing’s proportions.
x + y
115°
Choose an answer to try the example.
Why?
Explore the relationship
Make x exactly 20° larger than y.
In this drawing
Need a clue?
Their sum is 100°. Split that sum so the difference is 20°.
Example positions
Change x. The 80° angle stays fixed, so y changes by the same amount in the opposite direction.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
Further practice does not change your comparison score.
Continue your unfinished round
Your answers are saved in this tab. Continue from where you left off.
Continuing uses no additional practice start.
Discard the unfinished round?
Your answers from this round will be discarded. You can choose your settings before starting a new round.
Starting the new round uses one practice start.
- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Compare two quantitiesCompare two quantities using the given information. Then change the geometry to explore why the relationship holds.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used