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Exploring Triangle Perimeters and Circle Angle Relationships in Geometry

This guide covers essential topics in geometry, including calculating the perimeter of triangles with given side lengths and exploring angle relationships in circles based on the vertex's location—inside, on, or outside the circle. Through examples and exercises, students will learn to find angle measures and understand the significance of arcs and angles in various geometric configurations. Key concepts include triangle perimeter calculations, angle measures in circles, and different cases of vertex positioning. Perfect for students preparing for assessments!

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Exploring Triangle Perimeters and Circle Angle Relationships in Geometry

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  1. Warm-up A 1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. N M 50 C P 3. MCY = 270 Find BC. B 2. Find ACB 20 B A M 312 20 90 B 24 C C Y

  2. 6.5 Other Angle Relationships – On, Inside, and Outside of the Circle

  3. Case I:Vertex is ON the circle ANGLE ARC ARC ANGLE

  4. REMEMBER: Find m1. A B 1 124° C m1 = 62º

  5. Ex. 1: Find m1. 1 78° m1 = 39º

  6. 108° Ex. 2: Find m1. 1 m1 = 126º

  7. Case II:Vertex is inside the circle A ARC B ANGLE D ARC C Looks like a PLUS sign!

  8. Ex. 4 Find m1. 93° A B 1 D C 113° m1 = 103º

  9. Ex. 5 Find mQT. mQT = 100º N Q 84º 92º M T

  10. Case III:Vertex is outside the circle C ANGLE small ARC A D LARGE ARC B LARGE ARC LARGE ARC small ARC ANGLE small ARC ANGLE

  11. Ex. 6 Find m1. 1 15° A D 65° B m1 = 25º

  12. Ex. 7 Find mAB. mAB = 16º A 27° 70° B

  13. Ex. 8 Find m1. 260° 1 m1 = 80º

  14. 52.5º 4 32º 2 Brain Buster 3 105º 36.5º 1 105º 16º

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