Postulates & Theorems - chapter 8

Question 1

The altitude to the hypotenuse of a right triangle forms ….

Answer 1

two triangles that are similar to each other and to the original triangle. (theo. 8-1-1)

Question 2

GEOMETRIC MEANS COROLLARY: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of ….

Answer 2

the lengths of the two segments of the hypotenuse. (cor. 8-1-2)

Question 3

GEOMETRIC MEANS COROLLARY: The length of a leg of a right triangle is the geometric mean of ….

Answer 3

the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg. (cor. 8-1-3)

Question 4

THE LAW OF SINES: For any triangle ABC with sides a, b, and c, ….

Answer 4

(sinA)/a = (sinB)/b = (sinC)/c

Question 5

THE LAW OF COSINES: For any triangle ABC with sides a, b, and c, ….

Answer 5

a^2 = b^2 + c^2 - 2bc(cosA)
b^2 = a^2 + c^2 - 2ac(cosB)
c^2 = a^2 + b^2 - 2ab(cosC)