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(a) Since the sum of the measures of the interior is 360 , we add (x 10) (2x 20) (3x 50) (2x 20) 8x 40 x Then x 10 60; 2x 20 120; 3x 50 100; 2x 20 80. 360 360 50 Ans. 60 , 120 , 100 , 80



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(b) Let the exterior angles be represented respectively by 2x, 3x, 4x, and 6x. Then 2x 3x 4x 6x 360. Solving gives us 15x 360 and x 24. Hence, the exterior angles measure 48 , 72 , 96 , and 144 . The interior angles are their supplements. Ans. 132 , 108 , 84 , 36

Three methods of proving triangles congruent have already been introduced here. These are 1. Side-Angle-Side (SAS) 2. Angle-Side-Angle (ASA) 3. Side-Side-Side (SSS) Two additional methods of proving that triangles are congruent are 4. Side-Angle-Angle (SAA) 5. Hypotenuse-Leg (hy-leg)

PRINCIPLE 1:

MIME media type name: application MIME subtype name: xml-dtd Mandatory parameters: none Optional parameters: charset





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Endorsements When a check is given to the bank for deposit, the depositor signs the check to show that he or she accepts responsibility for the amount of that check. The depositor s signature is known as an endorsement. This en dorsement transfers the ownership of the check and guarantees to the in dividual that the depositor will guarantee its payment. Different kinds of endorsements serve different needs. 1. Blank endorsements. A blank endorsement consists only of the name of the endorser. Its disadvantage lies in the fact that a lost or stolen check with a blank endorsement may be cashed by the nder or thief.

(SAA) If two angles and a side opposite one of them of one triangle are congruent to the corresponding parts of another, the triangles are congruent.

Fig. 4-54

Fig. 4-55

PRINCIPLE 2:

(hy-leg) If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, the triangles are congruent.

4.18 Selecting congruent triangles using hy-leg or SAA In (a) Fig. 4-56 and (b) Fig. 4-57, select congruent triangles and state the reason for the congruency.

Fig. 4-56

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2 Endorsement in full Endorsement in full states that the check can be cashed or transferred only on the order of the person named in the en dorsement 3 Restrictive endorsement A restrictive endorsement limits the re ceiver of the check as to the use he or she can make of the funds collect ed Usually this type of endorsement is done when checks are prepared for deposit Reconciliation Each month, the bank forwards to the depositor a statement of his or her account showing the beginning balance, all the deposits made and other credits, any checks paid and other charges (debits), and the ending bal ance Included in this envelope with the statement are the paid or canceled checks and any other deductions or addi tions to the account.

Fig. 4-57

(a) ^ I > ^ II by hy-leg. In ^ III, 4 is not a hypotenuse. (b) ^ I > ^ III by SAA. In ^ II, 7 is opposite 60 instead of 35 . In ^ IV, 7 is included between 60 and 35 .

4.19 Determining the reason for congruency of triangles In each part of Fig. 4-58, ^ I can be proved congruent to ^ II. Make a diagram showing the congruent parts of both triangles and state the reason for the congruency.

Fig. 4-58

Fig. 4-59

Given: Quadrilateral ABCD DF ' AC, BE ' AC AE > FC, BC > AD To Prove: BE > FD Plan: Prove ^ I > ^ II

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