ssrs barcode font Parallel Lines, Distances, and Angle Sums in Objective-C

Creation QR in Objective-C Parallel Lines, Distances, and Angle Sums

CHAPTER 4 Parallel Lines, Distances, and Angle Sums
QR Recognizer In Objective-C
Using Barcode Control SDK for iPhone Control to generate, create, read, scan barcode image in iPhone applications.
QR Code 2d Barcode Drawer In Objective-C
Using Barcode encoder for iPhone Control to generate, create QR image in iPhone applications.
Fig. 4-71
Recognizing QR Code 2d Barcode In Objective-C
Using Barcode reader for iPhone Control to read, scan read, scan image in iPhone applications.
Barcode Maker In Objective-C
Using Barcode printer for iPhone Control to generate, create bar code image in iPhone applications.
Fig. 4-72
Paint QR Code In C#
Using Barcode creator for .NET framework Control to generate, create QR Code JIS X 0510 image in .NET framework applications.
Quick Response Code Creator In Visual Studio .NET
Using Barcode creation for ASP.NET Control to generate, create QR image in ASP.NET applications.
Provide the proofs requested in Fig. 4-73.
Quick Response Code Generation In .NET Framework
Using Barcode drawer for .NET Control to generate, create Denso QR Bar Code image in .NET applications.
Make QR Code In Visual Basic .NET
Using Barcode printer for .NET Control to generate, create Denso QR Bar Code image in .NET framework applications.
(4.20)
Data Matrix ECC200 Maker In Objective-C
Using Barcode maker for iPhone Control to generate, create ECC200 image in iPhone applications.
Create Bar Code In Objective-C
Using Barcode creation for iPhone Control to generate, create barcode image in iPhone applications.
Fig. 4-73
Print Bar Code In Objective-C
Using Barcode maker for iPhone Control to generate, create bar code image in iPhone applications.
UPC - 13 Encoder In Objective-C
Using Barcode creator for iPhone Control to generate, create EAN-13 Supplement 5 image in iPhone applications.
Prove each of the following:
UPC-E Supplement 5 Drawer In Objective-C
Using Barcode creation for iPhone Control to generate, create GS1 - 12 image in iPhone applications.
GS1-128 Maker In None
Using Barcode creator for Microsoft Word Control to generate, create UCC-128 image in Office Word applications.
(4.21)
Drawing UCC - 12 In Objective-C
Using Barcode printer for iPad Control to generate, create UCC-128 image in iPad applications.
Encoding ANSI/AIM Code 39 In None
Using Barcode generation for Online Control to generate, create Code 3 of 9 image in Online applications.
(a) If the perpendiculars to two sides of a triangle from the midpoint of the third side are congruent, then the triangle is isosceles. (b) Perpendiculars from a point in the bisector of an angle to the sides of the angle are congruent. (c) If the altitudes to two sides of a triangle are congruent, then the triangle is isosceles. (d) Two right triangles are congruent if the hypotenuse and an acute angle of one are congruent to the corresponding parts of the other.
1D Encoder In C#.NET
Using Barcode creator for .NET framework Control to generate, create 1D Barcode image in Visual Studio .NET applications.
Bar Code Creation In None
Using Barcode encoder for Software Control to generate, create barcode image in Software applications.
Parallelograms, Trapezoids, Medians, and Midpoints
UPC Code Reader In Java
Using Barcode scanner for Java Control to read, scan read, scan image in Java applications.
Making Bar Code In None
Using Barcode maker for Online Control to generate, create barcode image in Online applications.
5.1 Trapezoids
A trapezoid is a quadrilateral having two, and only two, parallel sides. The bases of the trapezoid are its parallel sides; the legs are its nonparallel sides. The median of the trapezoid is the segment joining the midpoints of its legs. Thus in trapezoid ABCD in Fig. 5-1, the bases are AD and BC, and the legs are AB and CD. If M and N are midpoints, then MN is the median of the trapezoid.
Fig. 5-1
An isosceles trapezoid is a trapezoid whose legs are congruent. Thus in isosceles trapezoid ABCD in Fig. 5-2 AB > CD. The base angles of a trapezoid are the angles at the ends of its longer base: /A and /D are the base angles of isosceles trapezoid ABCD.
Fig. 5-2
5.1A Trapezoid Principles
PRINCIPLE 1:
The base angles of an isosceles trapezoid are congruent.
Thus in trapezoid ABCD of Fig. 5-3 if AB > CD, then /A > /D.
CHAPTER 5 Parallelograms, Trapezoids, Medians, and Midpoints
Fig. 5-3
PRINCIPLE 2:
If the base angles of a trapezoid are congruent, the trapezoid is isosceles.
Thus in Fig. 5-3 if /A > /D, then AB > CD.
SOLVED PROBLEMS
5.1 Applying algebra to the trapezoid In each trapezoid in Fig. 5-4, find x and y.
Fig. 5-4
Solutions
(a) Since AD i BC, (2x Also, y 70 5) (x 110. 20 or x 10. 50 180 or y 130. 5) 180; then 3x 180 and x 60. 180 or y
(b) Since /A > /D, 5x 3x 20, so that 2x Since BC i AD, y (3x 20) 180, so y (c) Since BC i AD, 3x Since /D > /A, y 2x 180 or x 72. 36. 2x or y
Proof of a trapezoid principle stated in words Prove that the base angles of an isosceles trapezoid are congruent.
Isosceles trapezoid ABCD (BC i AD, AB > CD) To Prove: /A > /D Plan: Draw $ to base from B and C. Prove nI > II.
PROOF:
Given:
Statements 1. Draw BE ' AD and CF ' AD. 2. BC i AD, AB > CD 3. BE > CF 4. /1 > /2 5. nI > nII 6. /A > /D
Reasons 1. A ' may be drawn to a line from an outside point. 2. Given 3. Parallel lines are everywhere equidistant. Definition of congruent segments. 4. Perpendiculars form rt. . All rt. are congruent. 5. Hy-leg s 6. Corresponding parts of congruent n are congruent.
CHAPTER 5 Parallelograms, Trapezoids, Medians, and Midpoints
5.2 Parallelograms
A parallelogram is a quadrilateral whose opposite sides are parallel. The symbol for parallelogram is ~. Thus in ~ABCD in Fig. 5-5, AB i CD in AD i BC.
Fig. 5-5
If the opposite sides of a quadrilateral are parallel, then it is a parallelogram. (This is the converse of the above definition.) Thus if AB i CD and AD i BC, then ABCD is a ~.
5.2A Principles Involving Properties of Parallelograms
PRINCIPLE 1: PRINCIPLE 2:
The opposite sides of a parallelogram are parallel. (This is the definition.) A diagonal of a parallelogram divides it into two congruent triangles.
BD is a diagonal of ~ABCD in Fig. 5-6, so nI > nII.
Fig. 5-6
PRINCIPLE 3:
The opposite sides of a parallelogram are congruent.
Thus in ~ABCD in Fig. 5-5, AB > CD and AD > BC.
PRINCIPLE 4:
The opposite angles of a parallelogram are congruent.
Thus in ~ABCD, /A > /C and /B > /D.
PRINCIPLE 5:
The consecutive angles of a parallelogram are supplementary.
Thus in ~ABCD, /A is the supplement of both /B and /D.
PRINCIPLE 6:
The diagonals of a parallelogram bisect each other.
Thus in ~ABCD in Fig. 5-7, AE > EC and BE > ED .
Fig. 5-7
5.2B Proving a Quadrilateral is a Parallelogram
PRINCIPLE 7:
A quadrilateral is a parallelogram if its opposite sides are parallel.
Thus if AB i CD and AD i BC, then ABCD is a ~.
PRINCIPLE 8:
A quadrilateral is a parallelogram if its opposite sides are congruent.
Thus if AB > CD and AD > BC in Fig. 5-8, then ABCD is a ~.
CHAPTER 5 Parallelograms, Trapezoids, Medians, and Midpoints
Fig. 5-8
PRINCIPLE 9:
A quadrilateral is a parallelogram if two sides are congruent and parallel.
Thus if BC > AD and BC i AD in Fig. 5-8, then ABCD is a ~.
PRINCIPLE 10:
A quadrilateral is a parallelogram if its opposite angles are congruent.
Thus if /A > /C and /B > /D in Fig. 5-8, then ABCD is a ~.
PRINCIPLE 11:
A quadrilateral is a parallelogram if its diagonals bisect each other.
Thus if AE > EC and BE > ED in Fig. 5-9, then ABCD is a ~.
Fig. 5-9
SOLVED PROBLEMS
5.3 Applying properties of parallelograms Assuming ABCD is a parallelogram, find x and y in each part of Fig. 5-10.
Fig. 5-10
Solutions
(a) By Principle 3, BC By Principle 3, 2y AD 3x and CD AB 2x; then 2(2x 3x) 40, so that 10x 2 3x; then 2y 2 3(4), so 2y 14 or y 7. 2y 15 or y 3. Then x 110. 3y 9. 40 or x 4.
(b) By Principle 6, x 2y 15 and x 3y. Substituting 3y for x in the first equation yields 3y (c) By Principle 4, 3x 20 x By Principle 5, y (x 40)
Copyright © OnBarcode.com . All rights reserved.