Use the Law of Cosines to write an expression equivalent to a.

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  a = √(b² +c² -2bc·cos(A))

  a = √(c² -b²)

Step-by-step explanation:

For sides a, b, c, and opposite angles A, B, C, the general form of the law of cosines is ...

  a² = b² + c² -2bc·cos(A)

An expression for 'a' can be written by taking the square root.

  a = √(b² +c² -2bc·cos(A))

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If you recognize that cos(A) = b/c, then a substitution can be made:

  a = √(b² +c² -2(bc)(b/c)) = √(b² +c² -2b²)

  a = √(c² -b²) . . . . . . . same as the Pythagorean theorem

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step-by-step explanation:

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc