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Given: CD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC.Prove: a2=b2+c2−2bccosAFigure shows triangle A B C. Segment A B is the base and contains point D. Segment C D is shown forming a right angle. Segment C D is labeled h. Segment A B is labeled c. Segment B C is labeled a. Segment A C is labeled b. Segment A D is labeled x. Segment D B is labeled c minus x. Select from the drop-down menus to correctly complete the proof.Statement ReasonCD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC. Given△ACD and △BCD are right triangles. Definition of right trianglea2=(c−x)2+h2a2=c2−2cx+x2+h2Square the binomial.b2=x2+h2cosA=xbbcosA=xMultiplication Property of Equalitya2=c2−2c(bcosA)+b2a2=b2+c2−2bccosA Commutative Properties of Addition and Multiplication

Given CD is an altitude of ABCProve a2b2c22bccosAFigure shows triangle A B C Segment A B is the base and contains point D Segment C D is shown forming a right a class=
Given CD is an altitude of ABCProve a2b2c22bccosAFigure shows triangle A B C Segment A B is the base and contains point D Segment C D is shown forming a right a class=

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Solution:

The equation below is given as

[tex]a^2=(c-x)^2+h^2[/tex]

This represents the

PYTHAGOREAN THEOREM

The second equation is given below as

[tex]b^2=x^2+h^2[/tex]

This represents the

PYTHAGOREAN THEOREM

The third expression is given below as

[tex]\cos A=\frac{x}{b}[/tex]

This represents

Definition of cosine

The fourth expression is given below as

[tex]a^2=c^2-2c(bcosA)+b^2[/tex]

This represents

Substitution property of equality

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