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(a) Since AB > AD, 3x (b) Since BC > AB, 5y 7 6 20 or x y 9. Since nABD is equiangular it is equilateral, and so y 31. 2 Since CD > BC, x y 20 or x 231. 2 2(35 ) 70 . 20.

PROOF:

1. 2. 3. 4. 5. 6. 7.

Summary

Reasons 1. 2. 3. 4. 5. 6. 7. Given Given A midpoint divides a line into two congruent parts. A rectangle is equiangular. Opposite sides of a ~ are congruent. SAS s Corresponding parts of congruent n are congruent.



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5.9 Proving a special parallelogram problem stated in words Prove that a diagonal of a rhombus bisects each vertex angle through which it passes.

Rhombus ABCD AC is a diagonal. To Prove: AC bisects /A and /C. Plan: Prove (1) /1 and /2 are congruent to /3. (2) /3 and /4 are congruent to /1.

PROOF:

Given:

1. 2. 3. 4. 5. 6. 7.

Statements ABCD is a rhombus. AB > BC /1 > /3 BC i AD, AB i CD /2 > /3, /1 > /4 /1 > /2, /3 > /4 AC bisects /A and /C.

1. The most liquid asset and also the one most subject to theft and fraud is ______. 2. A check involves three parties: the _______, who writes the check;





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Reasons 1. 2. 3. 4. 5. 6. 7. Given A rhombus is equilateral. In a n, angles opposite congruent sides are congruent. Opposite sides of a ~ are i. Alternate interior of i lines are congruent. Things congruent to the same thing are congruent to each other. To divide into two congruent parts is to bisect.

Placing the 0s or 1s in position (from h at left) yields 11101101, which is the binary value for 237 decimal. Let s look at another example, this time for decimal 122. 122/128 = 0 122/64 = 1 58/32 = 1 26/16 = 1 10/8 = 1 2/4 = 0 2/2 = 1 (h) (g) (f) (e) (d) (c) (b) then then then then 122 64 = 58 58 32 = 26 26 16 = 10 10 8 = 2

PRINCIPLE 1:

If three or more parallels cut off congruent segments on one transversal, then they cut off congruent segments on any other transversal.

Thus if l1 i l2 i l3 in Fig. 5-19 and segments a and b of transversal AB are congruent, then segments c and d of transversal CD are congruent.

Fig. 5-19

PRINCIPLE 2:

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the _______, the bank on which it is drawn; and the _______, the person to whom it is to be paid. 3. The signature on the back of a check showing that the individual accepts responsibility for that amount is known as an ________. 4. Under the _______, a fund is established for a xed petty cash amount that is reimbursed by a single check for amounts expended. 5. If a proof of petty cash is impossible, the account _______ will have to be used. Answers: 1. cash; 2. drawer, drawee, payee; 3. endorsement; 4. imprest system; 5. Cash Short and Over

If a line is drawn from the midpoint of one side of a triangle and parallel to a second side, then it passes through the midpoint of the third side.

PRINCIPLE 3:

If a line joins the midpoints of two sides of a triangle, then it is parallel to the third side and its length is one-half the length of the third side.

Fig. 5-20

PRINCIPLE 4:

Fig. 5-21

The median of a trapezoid is parallel to its bases, and its length is equal to one-half of the sum of their lengths.

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