Relationships with triangles

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the Triangle Inequality Theorem?
Back
The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
2.
FLASHCARD QUESTION
Front
In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the possible range for side AC?
Back
According to the Triangle Inequality Theorem, AC must be greater than |AB - BC| and less than AB + BC. Therefore, AC must be greater than |10 - 17| = 7 inches and less than 10 + 17 = 27 inches. So, 7 < AC < 27.
3.
FLASHCARD QUESTION
Front
How do you determine the longest side of a triangle?
Back
The longest side of a triangle is opposite the largest angle. To find it, compare the measures of the angles.
4.
FLASHCARD QUESTION
Front
What is the relationship between the sides and angles of a triangle?
Back
In a triangle, the larger the side, the larger the opposite angle. Conversely, the smaller the side, the smaller the opposite angle.
5.
FLASHCARD QUESTION
Front
What is the formula for calculating the area of a triangle?
Back
The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.
6.
FLASHCARD QUESTION
Front
How can you identify the shortest side of a triangle?
Back
The shortest side of a triangle is opposite the smallest angle. To identify it, compare the measures of the angles.
7.
FLASHCARD QUESTION
Front
What is the significance of the angles in a triangle?
Back
The angles in a triangle determine the shape and type of triangle (acute, right, obtuse) and are crucial for applying the Triangle Inequality Theorem.
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