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(a) In Fig. 3-9(a) by SSS. (b) In Fig. 3-9(a) by SAS. (c) In Fig. 3-9(b) by ASA. (d) In Fig. 3-9(c) by ASA. (e) In Fig. 3-9(c) by SAS.

(a) If AD > BC, then nI (b) If /1 /4, then nI nII by SSS. nII by SAS. nII by ASA. nII by ASA. nII by SAS.

Selecting corresponding parts of congruent triangles In each part of Fig. 3-10, the equal parts needed to prove nI parts that are congruent.

Fig. 3-10



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Congruent corresponding sides lie opposite congruent angles. Congruent corresponding angles lie opposite congruent sides. (a) Opposite 45 , AC > DE, Opposite 80 , BC > DF. Opposite the side of length 12; /C (b) Opposite AB and CD, /3 /A /C. /3. Opposite BE and EC, /1 /4. Opposite /5 and /6, AB > CD. (c) Opposite AE and ED, /2 /2. Opposite BC and AD, /1 /D.





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The negotiability of a note receivable based upon its maturity value, en ables the holder to receive cash from the bank before the due date. This is known as discounting. Once the interest to be paid has been determined, the procedure for discounting a note is quite simple. The maturity value of a note is: 1. Maturity value = face of note + interest income where the face is the principal and interest income is computed as before. The holder of a note may discount it at the bank prior to its due date. He or she will receive the maturity value, less the discount, or interest charge imposed by the bank for holding the note for the unexpired portion of its term. In other words, 2. Discount = maturity value discount rate unexpired time, and 3. Net Proceeds = maturity value discount. For example, Mr. Ed holds a $400, 90-day, 12 percent note written by Mr. Bill on April 10. It is discounted at 12 percent on May 10. The in terest on the note amounts to $12. Hence: 1. Maturity value = $400 + $12 = $412 Since at the time of discounting, Mr. Ed has held the note for only 30 days, the bank will have to wait 60 days until it can receive the matu rity value. The discount charge is then 2. Discount = $412 (12/100) (60/360) = $8.24 and Mr. Ed receives 3. Net proceeds = $412 $8.24 = $403.76

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The RSAKeyValue element has two elds: Modulus and Exponent: SCHEMA: <element name="RSAKeyValue" type="ds:RSAKeyValueType"/> <complexType name="RSAKeyValueType"> <sequence> <element name="Modulus" type="ds:CryptoBinary"/> <element name="Exponent" type="ds:CryptoBinary"/> </sequence> </complexType> DTD: <!ELEMENT RSAKeyValue (Modulus, Exponent) > <!ELEMENT Modulus (#PCDATA) > <!ELEMENT Exponent (#PCDATA) > Use the RetrievalMethod element within KeyInfo to convey a reference to KeyInfo information stored at some other location (rather than in the current XML document itself). SCHEMA: <element name="RetrievalMethod" type="ds:RetrievalMethodType"/> <complexType name="RetrievalMethodType"> <sequence> <element name="Transforms" type="ds:TransformsType" minOccurs="0"/> </sequence> <attribute name="URI" type="anyURI"/> <attribute name="Type" type="anyURI" use="optional"/>

/4. Opposite common side BD,

Fig. 3-11

(a) Since nI nII, by SSS, corresponding angles are congruent. Hence, 2x or y 20. (b) Since nI and y 5 24 or x 20 12, and 3y 26 or x 6, 60

(c) Since nI nII, by ASA, corresponding sides are congruent. Then 2x 3y 8 and x 2y. Substituting 2y for x in the first of these equations, we obtain 2(2y) 3y + 8 or y 8. Then x 2y 16.

PROOF:

Statements 1. BF ' AC 2. /5 /6 3. BF > BF 4. BF ' DE 5. /1 is the complement of /3. /2 is the complement of /4. 6. /3 /4 7. /1 /2 8. nI nII 9. AF > FC 1. Given

Note!

2. $ form rt. ; rt. are 3. Reflexive property 4. Given 5. Adjacent angles are complementary if exterior sides are to each other. 6. Given 7. Complements of are 8. ASA s 9. Corresponding parts of congruent n are

Proving a congruency problem stated in words Prove that if the opposite sides of a quadrilateral are equal and a diagonal is drawn, equal angles are formed between the diagonal and the sides.

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