Given: CD is an altitude of triangle ABC. Prove: a^2 = b^2 +c^2 = 2bccos A
1 answer:
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) = 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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Answer:
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I hope this helps :)
