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Chapter 6

Chapter 6 . More About Triangles. 6-1. Medians. Objective: Identify medians in triangles. Median – a segment that joins a vertex of the triangle and the midpoint of the side opposite that vertex. 11. Your Turn. 5x - 4. 6x + 9. 7x - 1. SP = PT. RQ = QT 7x – 1 = 6x + 9.

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Chapter 6

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  1. Chapter 6 More About Triangles

  2. 6-1 Medians Objective: Identify medians in triangles.

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

  4. 11

  5. Your Turn

  6. 5x - 4 6x + 9 7x - 1 SP = PT RQ = QT 7x – 1 = 6x + 9 5x – 4 = PT -6x -6x 5(10) – 4 = PT x – 1 = 9 46 = PT +1 +1 x = 10

  7. centroid – the point in a triangle where the medians meet

  8. Y N P X Q M Z

  9. 6-2 Altitudes and Perpendicular Bisectors Objective: Identify altitudes and perpendicular bisectors in triangles.

  10. altitude – a perpendicular segment with one endpoint at a vertex and the other endpoint on the side opposite that vertex

  11. Altitude Altitude Not an altitude

  12. perpendicular bisector – a perpendicular line or segment that bisects a side of triangle Perpendicular bisector altitude Midpoint

  13. Tell whether each red line or segment is a perpendicular bisector of a side of the triangle.

  14. 6-3 Angle Bisectors of Triangles

  15. Objective: Identify and use angle bisectors in triangles. angle bisector – a segment that separates an angle of the triangle into two congruent angles

  16. 33°

  17. 5x = 2x + 15 -2x -2x 3x = 15 x = 5

  18. 6-4 IsoscelesTriangles

  19. Objective: Identify and use properties of isosceles triangles.

  20. x = 49° y = 90°

  21. 48° -6x -6x -5 = -2x AC = 4x = 4(2.5) = 10 -2 -2 2.5 = x BC = 6x - 5 = 6(2.5) - 5 = 10

  22. 6-5 Right Triangles

  23. Objective: Use tests for congruence of right triangles.

  24. Theorem 6-7 HA Theorem Words: If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding angle of another right triangle, then the triangles are congruent. Model: Symbols:

  25. Theorem 6-8 LA Theorem Words: If the one leg and an acute angle of one right triangle are congruent to the corresponding leg and angle of another right triangle, then the triangles are congruent. Model: Symbols:

  26. Postulate 6-1 HL Postulate Words: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. Model: Symbols:

  27. 6-6 The Pythagorean Theorem Objective: Use the Pythagorean Theorem and its converse.

  28. Postulate 6-9 Pythagorean Theorem Words: 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. Model: Symbols:

  29. c = 17

  30. -36 -36 12.6= b

  31. It is not a right triangle.

  32. Objective: Find the distance between two points.

  33. The Candle Shop is about 7.8 miles from Mill’s Market.

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