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Understanding Isosceles, Equilateral, and Right Triangles: Properties and Theorems

This chapter explores the key properties and theorems related to isosceles, equilateral, and right triangles. Students will learn about base angles, vertex angles, and the crucial Base Angles Theorem, which states that in an isosceles triangle, two sides are congruent, leading to congruent angles opposite those sides. The chapter also covers the Hypotenuse-Leg (HL) Congruence Theorem for right triangles. Through interactive assignments and practice problems, students will deepen their understanding of triangle congruence and the relationships between their angles and sides.

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Understanding Isosceles, Equilateral, and Right Triangles: Properties and Theorems

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  1. Chapter 4.6 Isosceles, Equilateral, and Right Triangles

  2. Objectives/Assignment • Use properties of isosceles and equilateral triangles • Use properties of right triangles • Assignment: 1-25 all

  3. Goal 1: Using Properties of Isosceles Triangles • The two angles in an isosceles triangle adjacent to the base of the triangle are called base angles. • The angle opposite the base is called the vertex angle.

  4. Theorem 4.6: Base Angles Theorem • If two sides of a triangle are congruent, then the angles opposite them are congruent. A C B

  5. Theorem 4.7: Converse to the Base Angles Theorem • If two angles of a triangle are congruent, then the sides opposite them are congruent. A C B

  6. Corollary to the Base Angles Theorem 4.6 • If a triangle is equilateral, then it is equiangular.

  7. Corollary to the Converse of the Base Angles Theorem 4.7 • If a triangle is equiangular, then it is equilateral.

  8. Examples C A C B A B A B C NO YES YES

  9. Goal 2: Using Properties of Right Triangles Theorem 4.8 Hypotenuse-Leg (HL) Congruence Theorem • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. A D B F C E

  10. Practice Problems • Find the measure of the missing angles and tell which theorems you used. B B C A 50° A C

  11. More Practice Problems Is there enough information to prove the triangles are congruent? S T U R V W

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