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If the opposite sides of a quadrilateral are congruent and a diagonal is drawn, congruent angles are formed between the diagonal and the sides. Quadrilateral ABCD AB > CD, BC > AD AC is a diagonal. To Prove: /1 /4, /2 /3 Plan: Prove nI nII

PROOF:

Given:

PRINCIPLE 1:

If two sides of a triangle are congruent, the angles opposite these sides are congruent. (Base angles of an isosceles triangle are congruent.)

The bank s discount rate happened to be equal to the interest rate, but this need not always be the case.

Fig. 3-12

PRINCIPLE 2:



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Hashing This is an algorithm that generates a unique numeric value based on the content of transaction data so that it can be veri ed by recipients using the same algorithm by comparing the value as sent to the value as calculated upon receipt (called a checksum) to ensure that content is unaltered Encryption and decryption Information may be sent in an illegible (encrypted) form between two (or more) parties On receipt, it can be decrypted using the appropriate key and returned to a legible form This is done by using an algorithm, such as hashing In practice, the process is as follows: 1 Every transform is made up of an algorithm attribute and holds any content parameters appropriate to the algorithm used.

Fig. 3-13

PRINCIPLE 3:





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Principle 3 is a corollary of Principle 1. A corollary of a theorem is another theorem whose statement and proof follow readily from the theorem.

Fig. 3-14

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If the issuer of a note does not make payment on the due date, the note is said to be dishonored. It is no longer negotiable, and the amount is charged back to Accounts Receivable. The reasons for transferring the dishonored notes receivable to the Accounts Receivable accounts are that the Notes Receivable account is then limited to current notes that have not yet matured and the Accounts Receivable account will then show the dishonoring of the note, giving a better picture of the transaction. For example, a $500, 60-day, 12 percent note written by F. Saltzman was dishonored on the date of maturity. The entry is: Accounts Receivable, F. Saltzman 510 Notes Receivable 500 Interest Income 10 Observe that the interest income is recorded and is charged to the customer s account. When a payee discounts a note receivable, he or she creates a con tingent (potential) liability. This occurs because there is a possibility that the maker may dishonor the note. Bear in mind that the payee has already received payment from the bank in advance of the maturity date. The pay ee is, therefore, contingently liable to the bank to make good on the amount (maturity value) in the event of default by the maker. Any protest fee arising from the default of the note is charged to the maker of the note and is added to the amount to be charged against his or her account.

PRINCIPLE 4:

Fig. 3-15

Applying principles 1 and 3 In each part of Fig. 3-16, name the congruent angles that are opposite congruent sides of a triangle.

Fig. 3-16

/3. Since BC > CD, /2

Applying principles 2 and 4 In each part of Fig. 3-17, name the congruent sides that are opposite congruent angles of a triangle.

Fig. 3-17

Important Point!

(a) Since m/a (b) Since /A (c) Since /1 (d) Since /A 55 , /a /D. Hence, BC > CD. /C, BD > CD. /4 /D, CD > AD > AC. /C, BD > CD. /1, AD > BD. Since /2 /3, AB > BC. Since /2 /1

/4, AB > BD > AD. Since /2

3.10 Applying isosceles triangle principles In each of Fig. 3-18(a) and (b), nI can be proved congruent to nII. Make a diagram showing the congruent parts of both triangles and state the congruency principle involved.

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