Triangles & shapes
Compare triangle sides, similar shapes and diagonals. Then reshape the figures to test your reasoning.
Triangle side constraints
1 comparison · No time limit · Explore after checking
Example
Example
Compare the third side using only the stated side lengths.
Review the comparison
Two sides of a nondegenerate triangle have lengths 5 and 5 units.
The included angle is not specified.
The included angle shown is one allowed example, not a given.
Length of the third side
√101 units
Choose an answer to try the example.
Why?
Explore the relationship
Make the third side exactly √50 units long.
In this drawing
Need a clue?
Look for a right triangle: 5² + 5² = 50.
Example positions
Open the hinge. The third side grows but stays shorter than the sum of the fixed sides.
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.
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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
Scale similar trianglesCompare triangle sides, similar shapes and diagonals. Then reshape the figures to test your reasoning.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
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