Pythagorean Theorem and Converse

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
+5
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the Pythagorean Theorem?
Back
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².
Tags
CCSS.8.G.B.8
2.
FLASHCARD QUESTION
Front
What is a right triangle?
Back
A right triangle is a triangle that has one angle measuring 90 degrees.
Tags
CCSS.4.G.A.2
3.
FLASHCARD QUESTION
Front
How do you determine if three side lengths can form a right triangle?
Back
To determine if three side lengths can form a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides (c² = a² + b²).
Tags
CCSS.8.G.B.8
4.
FLASHCARD QUESTION
Front
If a = 3 and b = 4, what is c?
Back
c = 5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).
Tags
CCSS.8.G.B.8
5.
FLASHCARD QUESTION
Front
What is the converse of the Pythagorean Theorem?
Back
The converse of the Pythagorean Theorem states that if a² + b² = c² for three sides, then the triangle is a right triangle.
Tags
CCSS.8.G.B.8
6.
FLASHCARD QUESTION
Front
If a = 6 and b = 8, does c = 10 form a right triangle?
Back
Yes, because 6² + 8² = 36 + 64 = 100, and 10² = 100.
Tags
CCSS.8.G.B.8
7.
FLASHCARD QUESTION
Front
What is the length of the hypotenuse if a = 12 and b = 16?
Back
c = 20 (using the Pythagorean Theorem: 12² + 16² = 144 + 256 = 400, so c = √400 = 20).
Tags
CCSS.8.G.B.8
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