Card 1 of 20
EasyStudy card 1
Prompt
Where is a right triangle's hypotenuse?
Answer
Opposite the \(90^\circ\) angle.
MathChapter 17: Triangles
Flashcards
Pythagorean Theorem and Special Right Triangles Flashcards
Twenty cards on right-triangle anatomy, Pythagorean reasoning, converse tests, and exact special ratios.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
State the Pythagorean Theorem.
Answer
\(a^2+b^2=c^2\), with c the hypotenuse.
Card 3 of 20
EasyStudy card 3
Prompt
What is the 45-45-90 side ratio?
Answer
\(1:1:\sqrt2\).
Card 4 of 20
EasyStudy card 4
Prompt
What is the 30-60-90 side ratio?
Answer
\(1:\sqrt3:2\).
Card 5 of 20
EasyStudy card 5
Prompt
Which side is opposite 30° in a 30-60-90 triangle?
Answer
The short leg, x.
Card 6 of 20
EasyStudy card 6
Prompt
Which side is opposite 60° in a 30-60-90 triangle?
Answer
The long leg, \(x\sqrt3\).
Card 7 of 20
EasyStudy card 7
Prompt
Which side is opposite 90° in a 30-60-90 triangle?
Answer
The hypotenuse, \(2x\).
Card 8 of 20
MediumStudy card 8
Prompt
Find the hypotenuse for legs 5 and 12.
Answer
13.
Card 9 of 20
MediumStudy card 9
Prompt
Find the missing leg when c=17 and a=8.
Answer
15.
Card 10 of 20
MediumStudy card 10
Prompt
How do you test the converse of Pythagorean?
Answer
Put the longest side as c and check whether the two smaller squares sum to c squared.
Card 11 of 20
MediumStudy card 11
Prompt
Does 9, 12, 15 form a right triangle?
Answer
Yes; \(9^2+12^2=15^2\).
Card 12 of 20
MediumStudy card 12
Prompt
A 45-45-90 leg is 7. Find the hypotenuse.
Answer
\(7\sqrt2\).
Card 13 of 20
MediumStudy card 13
Prompt
A 30-60-90 short leg is 6. Find the long leg.
Answer
\(6\sqrt3\).
Card 14 of 20
MediumStudy card 14
Prompt
A 30-60-90 hypotenuse is 18. Find the short leg.
Answer
9.
Card 15 of 20
MediumStudy card 15
Prompt
Why is a 45-45-90 triangle isosceles?
Answer
Its two acute angles are equal, so the opposite legs are equal.
Card 16 of 20
MediumStudy card 16
Prompt
What is the final operation after finding a squared missing side?
Answer
Take the positive square root.
Card 17 of 20
HardStudy card 17
Prompt
What is wrong with using c for a leg?
Answer
It puts the wrong side alone in the Pythagorean equation.
Card 18 of 20
HardStudy card 18
Prompt
When should an exact radical remain in an answer?
Answer
When no decimal is requested and the radical cannot be simplified away.
Card 19 of 20
HardStudy card 19
Prompt
How do composite right-triangle problems usually proceed?
Answer
Solve one triangle, transfer the shared side, then solve the next.
Card 20 of 20
HardStudy card 20
Prompt
What common mix-up gives 2x as a 45-45-90 hypotenuse?
Answer
Confusing its 1:1:√2 ratio with the 30-60-90 hypotenuse rule.
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