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(a) /ABC and /ADB (or /1). The angles may also be named by reversing the order of the letters: /CBA and /BDA. (b) /DBC (c) /ADC (d) /2 or /BDC (e) /3 or /ABD

1.6 Adding and subtracting angles In Fig. 1-23, find (a) m/AOC; (b) m/BOE; (c) the measure of obtuse /AOE.

Fig. 1-23

(a) m/AOC (b) m/BOE (c) m/AOE m/a m/b 360 m/b m/c (m/a 90 m/d m/b 35 35 m/c 125 45 50 130 360 220 140

m/d)

Note!



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1.7 Finding parts of angles 1 2 2 1 Find (a) 5 of the measure of a rt. /; (b) 3 of the measure of a st. /; (c) 2 of 31 ; (d) 10 of 70 20 .





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In Solved Problem 7.25, it is given that ABCD in a figure like Fig. 7-9 is a parallelogram, and we must AF AE prove that . To prove this proportion, it is necessary to find similar triangles whose sides are BC FB in the proportion. This can be done simply by selecting the triangle whose letters A, E, and F are in the numerators and the triangle whose letters B, C, and F are in the denominators. Hence, we would prove nAEF , nBCF. AE BC Suppose that the proportion to be proved is . In such a case, interchanging the means leads to AF FB AE AF . BC FB The needed triangles can then be selected based on the numerators and the denominators. AE AF Suppose that the proportion to be proved is . Then our method of selecting triangles could not AD FB be used until the term AD were replaced by BC. This is possible, because AD and BC are opposite sides of the parallelogram ABCD and therefore are congruent.

ALT-0150 ALT-0151 ALT-0152 ALT-0153 ALT-0154 ALT-0155 ALT-0156 ALT-0159 – — ˜ ™ š › œ Ÿ ~

PRINCIPLE 1: PRINCIPLE 2: PRINCIPLE 3:

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Corresponding angles of similar triangles are congruent (by the definition). Corresponding sides of similar triangles are in proportion (by the definition). Two triangles are similar if two angles of one triangle are congruent respectively to two angles of the other.

Fig. 7-10

PRINCIPLE 4:

If liabilities are to be assumed by the partnership, they are credited to the respective liability ac counts.

Two triangles are similar if an angle of one triangle is congruent to an angle of the other and the sides including these angles are in proportion.

PRINCIPLE 5:

PRINCIPLE 6:

Two right triangles are similar if an acute angle of one is congruent to an acute angle of the other (corollary of Principle 3). A line parallel to a side of a triangle cuts off a triangle similar to the given triangle.

PRINCIPLE 7:

Fig. 7-11

Fig. 7-12

Partnership pro ts and losses may be divided in any manner the partners may agree upon. In general, a partner may be expected to share in pro portion to the amount of capital and/or services he or she contributes. In

PRINCIPLE 8: PRINCIPLE 9:

Triangles similar to the same triangle are similar to each other. The altitude to the hypotenuse of a right triangle divides it into two triangles which are similar to the given triangle and to each other. Triangles are similar if their sides are respectively parallel to each other. Triangles are similar if their sides are respectively perpendicular to each other.

PRINCIPLE 10:

En dash Em dash Small tilde Trade mark sign Latin small letter s with caron Single right-pointing angle quotation mark Latin small ligature OE Latin capital letter Y with dieresis

PRINCIPLE 11:

Fig. 7-13

Fig. 7-14

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