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It does not do to dwell on dreams… and forget to live. -Dumbledore

(4.5) Isosceles and Equilateral Triangles. It does not do to dwell on dreams… and forget to live. -Dumbledore. (4.5) Isosceles and Equilateral Triangles. OBJ: To use and apply properties of isosceles triangles. Isosceles Triangles. The congruent sides are the LEGS .

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It does not do to dwell on dreams… and forget to live. -Dumbledore

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  1. (4.5) Isosceles and Equilateral Triangles It does not do to dwell on dreams… and forget to live. -Dumbledore

  2. (4.5) Isosceles and Equilateral Triangles OBJ: To use and apply properties of isosceles triangles.

  3. Isosceles Triangles The congruent sides are the LEGS. The third side is the BASE. The two congruent sides form the VERTEX ANGLE. The other two angles are the BASE ANGLES.

  4. Theorems  Theorem 4.3: Isosceles Triangle Theorem – If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

  5. Theorems  Theorem 4.4: CONVERSE of Isosceles Triangle Theorem – If two angles of a triangle are congruent, then the sides opposite the angles are congruent.

  6. Theorems  Theorem 4.5: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

  7. Proof of the Isosceles Triangle Theorem Statements Reasons Given Definition of Perpendicular Bisector 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Reflexive Property of Congruence SASCPCTC

  8. Applications Explain why each statement is true. Isosceles Triangle Theorem Since angle TRS is congruent to angle WVS by Corresponding angles and angle WVS is congruent to angle S, then angle TRS is also congruent to angle S by transitive property of congruence.So by the converse of the isosceles triangle theorem, segment TR is congruent to segment TS.

  9. Applications Find the value of y.

  10. Corollaries corollary – a statement that follows immediately from a theorem Corollary to Theorem 4.3: If a triangle is equilateral, then the triangle is equiangular. Corollary to Theorem 4.4: If a triangle is equiangular, then the triangle is equilateral.

  11. 4.5: Isosceles and Equilateral Triangles Homework: (4.5) Pg. 230; #1-13, 15, 20, 22, 28, 30 I don't know half of you half as well as I should like, and I like less than half of you half as well as you deserve. -Bilbo

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