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Step 1: Prove: All right angles are equal in measure. s Steps 2 Given: j A and j B are rt. j and 3: To Prove: mj A mj B Step 4: Plan: Since each angle equals 90 , the angles are equal in measure, using Post. 1: Things equal to the same thing are equal to each other. Steps 5 and 6:

String: :String(const String& str) : len(str.len) 1 data = new char[len+l]; memcpy(data, str.data, len+l);

This implementation includes three constructors: the default constructor with optional parameter size, a constructor that allows an object to be initialized with an ordinary C string, and the copy constructor. The second access function is named convert ( > because it actually converts from type String to char * type. The subscript function is named character ( ) because it returns one character in the string -the one indexed by the parameter i. 8.23 Implement a Matrix class for 2-by-2 matrices:

90 .

This loop is set up to execute 10 times, but the execution will be terminated if the current value of sum equals or exceeds 10. In this particular case, the execution will terminate within the fourth pass (because 1 + 2 + 3 + 4 = 10).

Include a default constructor, a copy constructor, an inverse ( ) function that returns the inverse of the matrix, a det ( ) function that returns the determinant of the matrix, a Boolean function i ss ingular ( ) that returns 1 or 0 according to whether the determinant is zero, and a print ( ) function.

2.14 Proving a theorem Use the proof procedure to prove that supplements of angles of equal measure have equal measure.

class Matrix { public: Matrix(double a=O, double b=O, double c=O, : a_(a) I b_(b) I c-(c) I d-(d) 1 1 Matrix(const Matrix& m) : a-(m-a-), b-(m.bJ, c (m-c.& d_hd_) double det() { return a-*d- - b-*c-; } int isSingular { return det() == 0; } Matrix inverse(); void print();

Step 1: Prove: Supplements of angles of equal measure have equal measure. Steps 2 Given: ja sup. j1, jb sup. j2 and 3: mj1 mj2 To Prove: mja mjb Step 4: Plan: Using the subtraction postulate, the equal angle measures may be subtracted from the equal sums of measures of pairs of supplementary angles. The equal remainders are the measures of the supplements.

double d=O )

Steps 5 and 6:

class Matrix {

public: Matrix(double a=O, double b=O, double c=O, : a_(a) I b-(b) f c-(c) I d W -t > Matrix(const Matrix& m) : a-b--->, bA-dO, c-(m.c 1, d (m-d > double det() { return a - *d -b - *c:; } int isSingular { return det() == 0; } Matrix inverse(); void print(); private: double a-, b-, c-, d-; 1; Matrix Matrix::inverse() { double k = l/d&(); Matrix temp(k*d-,-k*b-,-k*c-,k*a return temp; double d=O )

1. 2. 3. 4. 5. j a sup. j 1, j b sup. j 2 mj a mj 1 180 mj b mj 2 180 mj a mj 1 mj b mj 2 mj 1 mj 2 mj a mj b 1. 2. 3. 4. 5.

- );

Given s s Sup. j are j the sum of whose measures 180 . Things to the same thing each other. Given If s are subtracted from s, the differences are .

3.7 LOOPING WITH Do-Loop In addition to For-Next structures, Visual Basic also includes Do-Loop structures, which are convenient when the number of passes through a loop is not known in advance (as, for example, when a loop is required to continue until some logical condition has been satisfied). A Do-Loop structure always begins with a Do statement and ends with a Loop statement. However, there are four different ways to write a Do-Loop structure. Two of the forms require that a logical expression appear in the Do statement (i.e., at the beginning of the block); the other two forms require that the logical expression appear in the Loop statement (at the end of the block). The general forms of the Do-Loop structure are shown below. First form:

Matrix::print() tout << a- << ' << b- << '\n' << c- << << d- << \n ;