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Understanding Geometric Concepts in Triangles

Learn about medians, altitudes, and bisectors in triangles. Explore their differences and understand their significance in geometry. Practice solving triangle problems and identify key geometric points.

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Understanding Geometric Concepts in Triangles

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  1. Medians Altitudes Angle Bisctors

  2. Section: 6-1 Medians Picture: Both sides are congruent Median vertex to midpoint

  3. How many medians can a triangle have? Median vertex to midpoint

  4. Midpoint- • If you have a midpoint- then the segments on both sides are CONGRUENT! • That is why you will see the “tick marks” • For the measure of the entire line- add both sides! EQ: What are the differences between medians, altitudes, and perpendicular bisectors?

  5. M D P C 9 N 1. What is NC if NP = 18? 2. If DP = 7.5, find MP. 15

  6. You Try the Following: A B C D 14 E 1.What is ED if DC = 14? 2.What Is AC is BC is 9? 3.If BC = 3, find AC. 6

  7. So if you are given the length of the entire side, how do you find a missing segment? • If you are given the length of a segment, how to you find the entire side? • If you have a median- what do you know about each side?

  8. A E B D C If CD = 2x + 5, BD = 4x – 1, and AE = 5x –2, find BE. BD = CD AE = BE BE = 13 4x – 1= 2x + 5 BE = 5x – 2 BE = 5(3) – 2 2x = 6 x = 3

  9. The intersection of the medians is called the CENTROID. Draw the Picture: How many medians does a triangle have?

  10. Concurrent: • When three or more lines or segments meet at the same point.

  11. Quick Assessment • What is a median? • What is a centroid? • What does concurrent mean? • What is the vertex? • What is a midpoint? EQ: What are the differences between medians, altitudes, and perpendicular bisectors?

  12. Centroid Lab • Lab- With partners • Worksheet

  13. Section: 6-2 Altitude Picture: Altitude vertex to opposite side and perpendicular

  14. Altitude The altitude is the “true height” of the triangle. EQ: What are the differences between medians, altitudes, and perpendicular bisectors?

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

  16. 6-2 Perpendicular Bisector Both sides are congruent- make sure you see this or it is NOT a perpendicular bisector Picture: Perpendicular Bisector midpoint and perpendicular

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

  18. Can you have both? • Can it be both an altitude and perpendicular bisector? • Help Me Draw Examples:

  19. Quick Assessment • What is the difference between altitude and perpendicular bisector? • What is an altitude? • What is a perpendicular bisector? • How can the segment be both- altitude and perpendicular bisector? EQ: What are the differences between medians, altitudes, and perpendicular bisectors?

  20. Graphic Organizer • Compare and Contrast: Perpendicular Bisector Altitude Median Angle Bisector

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