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ssrs barcode font Parallel Lines, Distances, and Angle Sums in ObjectiveC
CHAPTER 4 Parallel Lines, Distances, and Angle Sums Decode QR Code ISO/IEC18004 In ObjectiveC Using Barcode Control SDK for iPhone Control to generate, create, read, scan barcode image in iPhone applications. Paint QR Code 2d Barcode In ObjectiveC Using Barcode drawer for iPhone Control to generate, create QR Code image in iPhone applications. Solutions
Decode QR Code 2d Barcode In ObjectiveC Using Barcode scanner for iPhone Control to read, scan read, scan image in iPhone applications. Draw Bar Code In ObjectiveC Using Barcode creation for iPhone Control to generate, create bar code image in iPhone applications. (a) Since P is on the bisector 4 j A, it is equidistant from AB and AC. Since Q is on the bisectors 4 j4 it is of of B, 4 equidistant from AB and BC. Since R is on the bisectors of j A and jB, it is equidistant from AB, BC, and 4 AC. R is the incenter of ^ ABC, that is, the center of its inscribed circle. (b) Since P is on the ' bisector of AB, it is equidistant from A and B. Since Q is on the ' bisector of AC, it is equidistant from A and C. Since R is on the ' bisectors of AB and AC, it is equidistant from A, B, and C. R is the circumcenter of ^ ABC, that is, the center of its circumscribed circle. Drawing QR Code In Visual C#.NET Using Barcode drawer for .NET framework Control to generate, create QR image in Visual Studio .NET applications. Making QRCode In VS .NET Using Barcode generator for ASP.NET Control to generate, create QRCode image in ASP.NET applications. 4.10 Applying principles 1, 3, 6, and 7 In each part of Fig. 434, find two points equidistant from the ends of a line segment, and find the perpendicular bisector determined by the two points. Draw QR Code ISO/IEC18004 In VS .NET Using Barcode encoder for .NET framework Control to generate, create QR Code image in .NET framework applications. QR Creator In Visual Basic .NET Using Barcode maker for .NET Control to generate, create QR Code image in .NET applications. Fig. 434 Code 3 Of 9 Creator In ObjectiveC Using Barcode encoder for iPhone Control to generate, create Code 3 of 9 image in iPhone applications. GTIN  12 Maker In ObjectiveC Using Barcode printer for iPhone Control to generate, create UCC  12 image in iPhone applications. Solutions
Encoding Bar Code In ObjectiveC Using Barcode generator for iPhone Control to generate, create bar code image in iPhone applications. Encoding Barcode In ObjectiveC Using Barcode maker for iPhone Control to generate, create barcode image in iPhone applications. (a) B and D are equidistant from A and C; hence, BE is the ' bisector of AC. (b) A and D are equidistant from B and C; hence, AD is the ' bisector of BC. (c) B and D are equidistant from A and C; hence, BD is the ' bisector of AC. A and C are equidistant from B and D; hence, AC is the ' bisector of BD. EAN8 Supplement 2 AddOn Creator In ObjectiveC Using Barcode creation for iPhone Control to generate, create EAN 8 image in iPhone applications. UPC A Decoder In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. 4.3 Sum of the Measures of the Angles of a Triangle
Code39 Decoder In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Code128 Generation In None Using Barcode generation for Font Control to generate, create Code 128B image in Font applications. The angles of any triangle may be torn off, as in Fig. 435(a), and then fitted together as shown in (b). The three angles will form a straight angle. We can prove that the sum of the measures of the angles of a triangle equals 180 by drawing a line through 4 one vertex of the triangle parallel to the side opposite the vertex. In Fig. 435(c), MN is drawn through B parallel to AC. Note that the measure of the straight angle at B equals the sum of the measures of the angles of ^ ABC; that is, a b c 180 . Each pair of congruent angles is a pair of alternate interior angles of parallel lines. Data Matrix Creation In ObjectiveC Using Barcode printer for iPad Control to generate, create Data Matrix ECC200 image in iPad applications. Code128 Drawer In VB.NET Using Barcode creation for VS .NET Control to generate, create Code 128A image in VS .NET applications. Fig. 435 Code 3/9 Drawer In None Using Barcode creator for Online Control to generate, create Code 39 Full ASCII image in Online applications. Bar Code Drawer In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create barcode image in ASP.NET applications. CHAPTER 4 Parallel Lines, Distances, and Angle Sums
4.3A Interior and Exterior Angles of a Polygon
An exterior angle of a polygon is formed whenever one of its sides is extended through a vertex. If each of the sides of a polygon is extended, as shown in Fig. 436, an exterior angle will be formed at each vertex. Each of these exterior angles is the supplement of its adjacent interior angle. Fig. 436 Thus, in the case of pentagon ABCDE, there will be five exterior angles, one at each vertex. Note that each exterior angle is the supplement of an adjacent interior angle. For example, mja mja 180 . 4.3B AngleMeasureSum Principles
PRINCIPLE
The sum of the measures of the angles of a triangle equals the measure of a straight angle or 180 .
mj B mjC 180 .
Thus in ^ ABC of Fig. 437, mj A
Fig. 437 PRINCIPLE 2: If two angles of one triangle are congruent respectively to two angles of another triangle, the remaining angles are congruent. Thus in ^ ABC and ^ A B C in Fig. 438, if jA > j A and jB > jB , then jC > jC .
Fig. 438 PRINCIPLE 3: The sum of the measures of the angles of a quadrilateral equals 360 .
mjB mjC mjD 360 .
Thus in quadrilateral ABCD (Fig. 439), mjA
Fig. 439 CHAPTER 4 Parallel Lines, Distances, and Angle Sums
PRINCIPLE 4: The measure of each exterior angle of a triangle equals the sum of the measures of its two nonadjacent interior angles. mjA mjB.
Thus in ^ ABC in Fig. 440, mjECB
Fig. 440 PRINCIPLE 5: The sum of the measures of the exterior angles of a triangle equals 360 .
mjb mjc 360 .
Thus in ^ ABC in Fig. 441, mj a
Fig. 441 PRINCIPLE 6: The measure of each angle of an equilateral triangle equals 60 .
60 , mj B 60 , and mj C 60 .
Thus if ^ ABC in Fig. 442 is equilateral, then mj A
Fig. 442 PRINCIPLE 7: The acute angles of a right triangle are complementary.
90 , then mj A mj B 90 .
Thus in rt. ^ ABC in Fig. 443, if mjC
Fig. 443 PRINCIPLE 8: The measure of each acute angle of an isosceles right triangle equals 45 .
90 , then mj A 45 and mj B 45 .
Thus in isos. rt. ^ ABC in Fig. 444, if mjC
Fig. 444 PRINCIPLE 9: A triangle can have no more than one right angle.
s 90 , then j A and j B cannot be rt. j
Thus in rt. ^ ABC in Fig. 443, if mjC
PRINCIPLE 10: A triangle can have no more than one obtuse angle.
Thus in obtuse ^ABC in Fig. 445, if jC is obtuse, then j A and jB cannot be obtuse angles.
Fig. 445 CHAPTER 4 Parallel Lines, Distances, and Angle Sums
Two angles are supplementary if their sides are respectively perpendicular to each other.
PRINCIPLE 11: Thus if l1 ' l3 and l2 ' l4 in Fig. 446, then ja > jb, and a and jc are supplementary.
Fig. 446 SOLVED PROBLEMS
4.11 Numerical applications of anglemeasuresum principles In each part of Fig. 447, find x and y.
Fig. 447 Solutions
(a) x y 35 110 70 x 25 y 180 75 180 45 (Pr. 1) (Pr. 1) (c) In ^ABC, x In ^ I, x 25
y y y
65 x 90 90 65 90 25 (Pr. 7) (Pr. 7) Check: The sum of the measures of the angles of quad. ABCD should equal 360 . 70 120 110 60 360
360 360 (Pr. 4) (b) x is ext. j of ^ I. x 30 40 x y y 70 mjB 85 40 40 125 y is an ext. j of ^ABC.
(d) Since DC ' EB, x 90 x y 120 360 90 y 120 360 y 150 (e) Since AB iDE, x y x 50
4 4 4 (Pr. 7) 50 (Pr. 4) 45 45 (Pr. 4) 95 80 2x 180 100 (Pr. 4) 130 (f) Since AB iCD, 2x x y y 50 x 80 50 80
CHAPTER 4 Parallel Lines, Distances, and Angle Sums
4.12 Applying anglemeasuresum principles to isosceles and equilateral triangles Find x and y in each part of Fig. 448. Fig. 448 Solutions
(a) Since AB > AC, we have j1 > jx x 180 125 55 2x y 180 (Pr. 1) 110 y 180 y 70 (c) Since AB > AC, jABC > jACB 2x 80 180 (Pr. 1) x 50 1 1 In ^ I, 2x 2x y 180 (Pr. 1) x 50 (Pr. 6) (Pr. 8) y y y 180 180 130

