Triangles: Properties, Types & Key Theorems: 18 flashcards
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1. What is a triangle?
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A closed figure with three sides and three angles.
2. What is the sum of the interior angles of any triangle?
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$180^\circ$
3. What are the three types of triangles classified by sides?
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Equilateral, isosceles, and scalene.
4. What are the three types of triangles classified by angles?
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Acute, right, and obtuse.
5. In an equilateral triangle, what is each angle?
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$60^\circ$
6. What is true about the base angles of an isosceles triangle?
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They are equal.
7. State the triangle inequality.
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The sum of any two sides must be greater than the third side.
8. State the Pythagorean theorem.
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$a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
9. What is the hypotenuse?
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The longest side of a right triangle, opposite the right angle.
10. Can a triangle have two obtuse angles?
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No, because the sum would exceed $180^\circ$.
11. What does SSS stand for in congruence?
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Side-Side-Side: all three sides are equal.
12. What does SAS stand for in congruence?
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Side-Angle-Side: two sides and the included angle are equal.
13. What does RHS stand for in congruence?
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Right angle-Hypotenuse-Side: for right triangles only.
14. What are similar triangles?
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Triangles with equal corresponding angles and proportional sides.
15. Why are triangles used in bridges and cranes?
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Triangles are rigid and cannot be deformed without changing a side length, giving stability.
16. What is triangulation used for?
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Locating positions using angles from known points, as in GPS and navigation.
17. Does the Pythagorean theorem apply to all triangles?
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No, only to right triangles.
18. What is the angle sum proof based on?
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Parallel lines and alternate interior angles forming a straight line.
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