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Chapter 6

Chapter 6. More About Triangles. Section 6-1. Medians. Median. Is a segment in a triangle that joins a vertex of the triangle and the midpoint of the side opposite that vertex. Centroid. The medians of a triangle intersect at a common point called the centroid. Concurrent.

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Chapter 6

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  1. Chapter 6 More About Triangles

  2. Section 6-1 Medians

  3. Median Is a segment in a triangle that joins a vertex of the triangle and the midpoint of the side opposite that vertex

  4. Centroid The medians of a triangle intersect at a common point called the centroid.

  5. Concurrent When three or more lines or segments meet at the same point, they are concurrent.

  6. Theorem 6-1 The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.

  7. Section 6-2 Altitudes and Perpendicular Bisectors

  8. Altitude A perpendicular segment in which one endpoint is at a vertex and the other endpoint is on the side opposite that vertex.

  9. Perpendicular Bisector A segment or line that contains the midpoint of the side of a triangle and is perpendicular to that side.

  10. Section 6-3 Angle Bisectors of Triangles

  11. Angle Bisector A ray whose endpoint is the vertex and is located in the interior of the angle that separates a given angle into two angles with equal measure

  12. Section 6-4 Isosceles Triangles

  13. Theorem 6-2 If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

  14. Theorem 6-3 The median from the vertex angle of an isosceles triangle lies on the perpendicular bisector of the base and the angle bisector of the vertex angle.

  15. Theorem 6-4 If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

  16. Section 6-5 Right Triangles

  17. Hypotenuse The side opposite the right angle

  18. Legs The two sides that form the right angle

  19. Theorem 6-6 If two legs of one right triangle are congruent to the corresponding legs of another right triangle then the triangles are congruent.

  20. Section 6-6 The Pythagorean Theorem

  21. Pythagorean Theorem 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 legs a and b.

  22. Section 6-7 Distance on the Coordinate Plane

  23. Distance Formula If d is the distance between two points (x1, y1) and (x2, y2), then d = (x2 – x1)2 + (y2 – y1)2

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