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Understanding Isosceles Triangles: Definitions, Theorems, and Proofs

Learn about isosceles triangles, their properties, theorems, and proofs. Explore angles, sides, and key concepts for geometry.

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Understanding Isosceles Triangles: Definitions, Theorems, and Proofs

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  1. Lesson 6-4 Isosceles Triangles

  2. Ohio Content Standards:

  3. Ohio Content Standards: Formally define geometric figures.

  4. Ohio Content Standards: Formally define and explain key aspects of geometric figures, including:a. interior and exterior angles of polygons;b. segments related to triangles (median, altitude, midsegment);c. points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter);d. circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle).

  5. Isosceles Triangle:

  6. Isosceles Triangle: A triangle that has a least two congruent sides.

  7. Isosceles Triangle: The congruent sides are called legs.

  8. Isosceles Triangle: The side opposite the vertex angle is called the base.

  9. Isosceles Triangle: Vertex Angle Leg Leg Base Angles Base

  10. Theorem 6-2Isosceles Triangle Theorem

  11. Theorem 6-2Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

  12. Find the values of the variables. x° 35° y° 45°

  13. Theorem 6-4Converse of Isosceles Triangle Theorem

  14. Theorem 6-4Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

  15. E 2 3x - 3 1 D F 2x + 2

  16. Assignment:Pgs. 249 – 2506-14 all19-21 all

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