Explanation:
For a theorem that says "if A then B", the converse is "if B then A."
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The hing.e theorem has numerous parts to the hypothesis. Its converse retains many of those conditions, swapping only the relation between the included angle and the third side.
<u>theorem</u>: if two sides of one triangle are congruent to two sides of another, then the longest third side will be opposite the largest included angle.
<u>converse</u>: if two sides of one triangle are congruent to two sides of another, then the largest included angle will be opposite the longest third side.
Instead of relating the third side to the angle measure, the converse relates the angle measure to the third side.
Answer:
-11
Step-by-step explanation:
-5 minus 6 equals -11. Look up on Google
Answer:
A is your answer
Step-by-step explanation:
The sides of the triangle are given as 1, x, and x².
The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.
Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.
Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.
Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.
Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.
