emilybassett1970
Answered

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Given: CD is an altitude of triangle ABC.
Prove: a^2 = b^2 +c^2 = 2bccos A

Given CD Is An Altitude Of Triangle ABC Prove A2 B2 C2 2bccos A class=

Sagot :

Answer:

Step-by-step explanation:

                          Statements                                 Reasons

1). CD is an altitude of ΔABC                1). Given

2). ΔACD and ΔBCD are right              2). Definition of right triangles.

    triangles.

3). a² = (c - x)² + h²                                 3). Pythagoras theorem

4). a² = c² + x² - 2cx + h²                       4). Square the binomial.

5). b² = x² + h²                                       5). Pythagoras theorem.

6). cos(x) = [tex]\frac{x}{a}[/tex]                                           6). definition of cosine ratio for an angle

7). bcos(A) = x                                        7). Multiplication property of equality.

8). a² = c² - 2c(bcosA) + b²                    8). Substitution property

9). a² = b² + c² - 2bc(cosA)                    9). Commutative properties of

                                                                    addition and multiplication.

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