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Statements (a) Perpendiculars form right angles. (b) Complements of the same angle are congruent. (c) An equilateral triangle is equiangular. (d) A right triangle has only one right angle. (e) A triangle is not a quadrilateral.

Conclusion (predicate) form right angles are congruent is equiangular has only one right angle is not a quadrilateral



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For the sake of simplicity, interest is commonly computed on the basis of a 360-day year divided into 12 months of 30 days each. Two widely used methods are the cancellation method and the 6 percent, 60-days method. The Cancellation Method Consider a note for $400 at 6 percent for 90 days. The principal is the face amount of the note ($400). The rate of interest is written as a fraction: 6/100. The time, if less than a year, is expressed as a fraction by dividing the number of days the note runs by the number of days in a year: 90/360. Thus Interest = $400 (6/100) (90 /360) = $6 The 6 Percent, 60-Days Method The 6 percent, 60-days Method is a variation of the cancellation method, based on the fact that 60 days, or 1/6 of a year, at 6 percent is equivalent to 1 percent, so that the interest is obtained by shifting the decimal point of the principal two places to the left.





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2.12 Determining the hypothesis and conclusion in if-then form Determine the hypothesis and conclusion of each statement. Solutions Hypothesis (if clause) Conclusion (then clause) If a line bisects an angle then it divides the angle into two congruent parts If it is an obtuse triangle (then) a triangle has an obtuse angle If a student is sick (then) she should not go to school If he wishes to pass (then) a student must study regularly

Statements (a) If a line bisects an angle, then it divides the angle into two congruent parts. (b) A triangle has an obtuse angle if it is an obtuse triangle. (c) If a student is sick, she should not go to school. (d) A student, if he wishes to pass, must study regularly.

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2.13 Forming converses and determining their truth State whether the given statement is true. Then form its converse and state whether this is necessarily true. (a) A quadrilateral is a polygon. (b) An obtuse angle has greater measure than a right angle. (c) Florida is a state of the United States. (d) If you are my pupil, then I am your teacher. (e) An equilateral triangle is a triangle that has all congruent sides.

(a) Statement is true. Its converse, a polygon is a quadrilateral, is not necessarily true; it might be a triangle. (b) Statement is true. Its converse, an angle with greater measure than a right angle is an obtuse angle, is not necessarily true; it might be a straight angle. (c) Statement is true. Its converse, a state of the United States is Florida, is not necessarily true; it might be any one of the other 49 states. (d) Statement is true. Its converse, if I am your teacher, then you are my pupil, is also true. (e) The statement, a definition, is true. Its converse, a triangle that has all congruent sides is an equilateral triangle, is also true.

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