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1.5 Special Points in Triangles

1.5 Special Points in Triangles. Warm-Up: How many times can you subtract the number 5 from 25?. Objectives: Discover points of concurrency in triangles. Draw the inscribed and circumscribed circles of triangles.

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1.5 Special Points in Triangles

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  1. 1.5 Special Points in Triangles Warm-Up: How many times can you subtract the number 5 from 25? Objectives: Discover points of concurrency in triangles. Draw the inscribed and circumscribed circles of triangles. Once. After the first calculation you will be subtracting 5 from 20, then 5 from 15, and so on. If you divide thirty by a half and add ten, what is the answer? 70. When dividing by fractions, you must invert and multiply.

  2. Vocabulary: Inscribed Circle: A circle in the inside of a triangle that touches each side at one point. (a circle is inscribed in a polygon if each side of the polygon is tangent to the circle)

  3. Vocabulary: Circumscribed Circle: A circle that is drawn around the outside of a triangle and contains all three vertices. (a circle is circumscribed about a polygon if each vertex of the polygon lies on the circle)

  4. Vocabulary: Concurrent: Literally “running together” of three or more lines intersecting at a single point.

  5. Vocabulary: Incenter: The center of a inscribed circle; the point where the three angle bisectors intersect. (It is equidistant from the three sides of the triangle).

  6. Vocabulary: Circumcenter: The center of a circumscribed circle where the three perpendicular bisectors of the sides of a triangle intersect. (It is equidistant from the three vertices of the triangle).

  7. Example 1: Label the inscribed circle, circumscribed circle, the incenter, the circumcenter, and points of concurrency in the following figures. circumscribed circle inscribed circle points of concurrency incenter circumcenter

  8. Example 2: Find the perpendicular bisector of each side ofXYZ . Y Z X

  9. Example 3: Find the angle bisectors of each angle of LMN . M L N

  10. Example 4: Find the circumscribed circle of JKL. K L J To find identify the perpendicular bisectors of the triangles sides.

  11. Example 5: Find the inscribed circle of MNO. N O M To find identify the angle bisectors of the triangle.

  12. Example 6: Find the circumscribed circle of . A B C To find identify the perpendicular bisectors of the triangles sides.

  13. Example 7: Find the inscribed circle of WXY. X Y W To find identify the angle bisectors of the triangle.

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