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4-6 Isosceles, Equilateral and Right Triangles

4-6 Isosceles, Equilateral and Right Triangles. Parts of Isosceles Triangles. Legs of an Isosceles T riangle – The congruent sides of an isosceles triangle Base of an I sosceles Triangle – The non-congruent side of an isosceles triangle

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4-6 Isosceles, Equilateral and Right Triangles

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  1. 4-6Isosceles, Equilateral and Right Triangles

  2. Parts of Isosceles Triangles Legs of an Isosceles Triangle – The congruent sides of an isosceles triangle Base of an Isosceles Triangle – The non-congruent side of an isosceles triangle Vertex Angle – The angle formed by the legs in an isosceles triangle Base Angles – The angles opposite the legs in an isosceles triangle

  3. H Vertex Angle Leg Leg Base Angles P I Base

  4. The Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent If two angles of a triangle are congruent, then the sides opposite those angles are congruent

  5. Informal Proof of the Isosceles Triangle Theorem: H • Draw auxiliary segment that bisects • Two triangles are congruent by • by SSS CPCTC I P H • Draw auxiliary segment that bisects • Two triangles are congruent by • by AAS CPCTC P I

  6. Corollary - A true statement that follows immediately from a theorem • Corollaries following the Isosceles Triangle Theorem • If a triangle is equilateral, then it is equiangular • If a triangle is equiangular, then it is equilateral

  7. Parts of Right Triangles Hypotenuse of a Right Triangle – The side opposite the right angle in a right triangle Legs of a Right Triangle – The sides that form the right angle in a right triangle D Hypotenuse Leg J M Leg

  8. Hypotenuse-Leg Theorem HL Theorem If the hypotenuse and the leg of a right triangle are congruent to the hypotenuse and the leg of another right triangle, then the two triangles are congruent

  9. Informal Proof of the HL Theorem: ● • Draw auxiliary . Mark point S so that . • by • by • by • by • by SAS CPCTC CPCTC AAS Theorem

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