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Congruent figures are figures that have the same size and the same shape; they are the exact duplicates of each other. Such figures can be moved on top of one another so that their corresponding parts line up exactly. For example, two circles having the same radius are congruent circles. Congruent triangles are triangles that have the same size and the same shape. If two triangles are congruent, their corresponding sides and angles must be congruent. Thus, congruent triangles ABC and ArBrCr in Fig. 3-1 have congruent corresponding sides (AB ArCr , BC BrCr , and /Cr). AC ArCr ) and congruent corresponding angles (/A /Ar, /B /Br, and /C



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Fig. 3-1

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(Read nABC nArBrCr as Triangle ABC is congruent to triangle A-prime, B-prime, C-prime. ) Note in the congruent triangles how corresponding equal parts may be located. Corresponding sides lie opposite congruent angles, and corresponding angles lie opposite congruent sides.

PRINCIPLE 1:

If two triangles are congruent, then their corresponding parts are congruent. (Corresponding parts of congruent triangles are congruent.)

Fig. 3-2

PRINCIPLE 2:

(Side-Angle-Side, SAS) If two sides and the included angle of one triangle are congruent to the corresponding parts of another, then the triangles are congruent.





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2. Settle an open account There are times when a note is issued in settlement of an account payable. Assume that the Julie Agency bought merchandise from the Josh Corpo ration for $500 and at the end of the month, the account balance remained in full. If the Julie Agency is unable to pay, they may issue a note to the Josh Corporation for the $500 account payable, converting the account payable into a note payable. Note that the Julie Agency still owes the debt to Josh Corporation. However, it now becomes a different form of obli gation, as it is a written, signed promise in the form of a note payable. 3. Borrow money from a bank On occasion, businesses nd it necessary to borrow money by giving a note payable to a bank. Frequently, banks require the interest be paid in advance. This is accomplished by deducting the amount of the interest from the principal when the loan is made and is known as discounting a note payable. The proceeds will be that amount of money that the maker of the note receivable receives after the discount has been taken from the principal. Notes Receivable A note received from a customer is an asset because it becomes a claim against the buyer for the amount due. Assume that Howard Cogan owes David Smith $400 and gives him a 90-day, 15 percent note in settlement. Mr. Cogan still owes the debt, but his obligation is of a different type now. On Mr. Smith s books the entry is: Notes Receivable 400

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Fig. 3-3

PRINCIPLE 3:

(Angle-Side-Angle, ASA) If two angles and the included side of one triangle are congruent to the corresponding parts of another, then the triangles are congruent.

Fig. 3-4

PRINCIPLE 4:

(Side-Side-Side, SSS) If three sides of one triangle are congruent to three sides of another, then the triangles are congruent.

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Fig. 3-5

Only the principal ($400) is recorded when the note is received, since it represents the amount of the unpaid account. The interest is not due un til the date of collection, 90 days later. At that time, the interest earned will be part of the entry recognizing the receipt of the proceeds from the note: Cash 415

Selecting congruent triangles From each set of three triangles in Fig. 3-6 select the congruent triangles and state the congruency principle that is involved.

(a) nI (b) nII (c) nI nII, by SAS. In nIII, the right angle is not between 3 and 4. nIII, by ASA. In nI, side 10 is not between 70 and 30 . nII nIII by SSS.

Fig. 3-6

Determining the reason for congruency of triangles In each part of Fig. 3-7, nI can be proved congruent of nII. Make a diagram showing the equal parts of both triangles and state the congruency principle that is involved.

Fig. 3-7

Fig. 3-8

Interest Income* 15

Finding parts needed to prove triangles congruent State the additional parts needed to prove nI nII in the given figure by the given congruency principle.

Fig. 3-9

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