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Triangles & Polygons

136 cards · 🇺🇸 English

Triangle properties/theorems plus quadrilaterals and other polygons.

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Triangle

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  1. 1Triangle
    A polygon with three corners (vertices) and three sides (edges)
  2. 2How many internal angles does a triangle have?
    Three
  3. 3Sum of the internal angles of a triangle
    180 degrees (or π radians)
  4. 4Equilateral triangle
    A triangle with all three sides equal in length
  5. 5Isosceles triangle
    A triangle with two sides of equal length
  6. 6Scalene triangle
    A triangle with three different-length sides
  7. 7Right triangle
    A triangle with one 90-degree (right) angle
  8. 8Acute triangle
    A triangle where all three angles are less than 90 degrees
  9. 9Obtuse triangle
    A triangle with one angle greater than 90 degrees
  10. 10Do equilateral triangles have equal angles?
    Yes, all three angles are 60 degrees
  11. 11In an isosceles triangle, what can you say about angles?
    The two angles opposite the equal sides are also equal
  12. 12Base of a triangle
    A chosen side (often the bottom), with the opposite vertex called the apex
  13. 13Height (altitude) of a triangle
    The perpendicular distance from the base to the opposite vertex
  14. 14Area formula for a triangle
    Area = (1/2) × base × height
  15. 15If a triangle has base 6 and height 4, what is its area?
    12 (calculated as 1/2 × 6 × 4)
  16. 16Triangle inequality
    The sum of any two sides must be greater than the third side
  17. 17Can a triangle have sides 3, 4, and 10?
    No, because 3 + 4 < 10 (violates triangle inequality)
  18. 18Perimeter of a triangle
    The sum of the lengths of all three sides
  19. 19Perpendicular bisector
    A line passing through the midpoint of a side and perpendicular to it
  20. 20Where do the three perpendicular bisectors meet?
    At the circumcenter
  21. 21Circumcenter
    The center of the circumcircle, the circle passing through all three vertices
  22. 22Circumcircle
    The circle passing through all three vertices of a triangle
  23. 23Altitude in a triangle
    A perpendicular line from a vertex to the opposite side (or its extension)
  24. 24Where do the three altitudes intersect?
    At the orthocenter
  25. 25Orthocenter
    The point where the three altitudes of a triangle intersect
  26. 26The orthocenter in an acute triangle
    Inside the triangle
  27. 27The orthocenter in a right triangle
    At the vertex with the right angle
  28. 28The orthocenter in an obtuse triangle
    Outside the triangle
  29. 29Angle bisector
    A line that divides an angle into two equal angles
  30. 30Where do the three angle bisectors meet?
    At the incenter

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