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Warm up: Solve for x.

Warm up: Solve for x. Linear Pair. 4x + 3 . 7x + 12. X = 15. Special Segments in Triangles. Median. Connect vertex to opposite side's midpoint. Altitude. Connect vertex to opposite side and is perpendicular. Tell whether each red segment is an altitude of the triangle.

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Warm up: Solve for x.

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  1. Warm up: Solve for x. Linear Pair 4x + 3 7x + 12 X = 15

  2. Special Segments in Triangles

  3. Median Connect vertex to opposite side's midpoint

  4. Altitude Connect vertex to opposite side and is perpendicular

  5. Tell whether each red segment is an altitude of the triangle. The altitude is the “true height” of the triangle. YES NO YES

  6. Perpendicular Bisector Goes through the midpoint and is perpendicular

  7. Tell whether each red segment is an perpendicular bisector of the triangle. NO NO YES

  8. Angle Bisector Cuts the angle In to TWO congruent parts

  9. Start to memorize… • Indicate the special triangle segment based on its description

  10. Who am I? I cut an angle into two equal parts Angle Bisector

  11. Who am I? I connect the vertex to the opposite side’s midpoint Median

  12. Who am I? I connect the vertex to the opposite side and I’m perpendicular Altitude

  13. Who am I? I go through a side’s midpoint and I am perpendicular Perpendicular Bisector

  14. Drill & Practice • Indicate which special triangle segment the red line is based on the picture and markings

  15. Multiple ChoiceIdentify the red segment Q1: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  16. Multiple ChoiceIdentify the red segment Q2: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  17. Multiple ChoiceIdentify the red segment Q3: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  18. Multiple ChoiceIdentify the red segment Q4: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  19. Multiple ChoiceIdentify the red segment Q5: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  20. Multiple ChoiceIdentify the red segment Q6: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  21. Multiple ChoiceIdentify the red segment Q7: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  22. Multiple ChoiceIdentify the red segment Q8: • Angle Bisector B. Altitude • C. Median D. Perpendicular Bisector

  23. Points of Concurrency

  24. New Vocabulary(Points of Intersection) Centroid Orthocenter Incenter Circumcenter

  25. Point of Intersection Medians intersect at the centroid

  26. Important Info about the Centroid • The intersection of the medians. • Found when you draw a segment from one vertex of the triangle to the midpoint of the opposite side. • The center is two-thirds of the distance from each vertex to the midpoint of the opposite side. • Centroid always lies inside the triangle. • This is the point of balance for the triangle.

  27. The intersection of the medians is called the CENTROID.

  28. Point of Intersection Altitudes intersect at the orthocenter

  29. Important Info about the Orthocenter • This is the intersection point of the altitudes. • You find this by drawing the altitudes which is created by a vertex connected to the opposite side so that it is perpendicular to that side. • Orthocenter can lie inside (acute), on (right), or outside (obtuse) of a triangle.

  30. The intersection of the altitudes is called the ORTHOCENTER.

  31. Point of Intersection Angle Bisector intersect at the incenter

  32. Important Info about the Incenter • The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle. • Incenter is equidistant from the sides of the triangle. • The center of the triangle’s inscribed circle. • Incenter always lies inside the triangle

  33. The intersection of the angle bisectors is called the INCENTER.

  34. Point of Intersection Perpendicular Bisectors intersect at the circumcenter

  35. Important Information about the Circumcenter • The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle. • The circumcenter is the center of a circle that surrounds the triangle touching each vertex. • Can lie inside an acute triangle, on a right triangle, or outside an obtuse triangle.

  36. The intersection of the perpendicular bisector is called the CIRCUMCENTER.

  37. MC AO ABI PBCC Medians/Centroid Altitudes/Orthocenter Angle Bisectors/Incenter Perpendicular Bisectors/Circumcenter Memorize these!

  38. MC AO ABI PBCC My Cousin Ate Our Avocados But I Prefer Burritos Covered in Cheese Will this work?

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