 3.6.1: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.2: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.3: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.4: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.5: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.6: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.7: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.8: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.9: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.10: Construction In Exercises 110, first sketch and label the figure yo...
 3.6.11: Technology Using geometry software, draw a large scalene obtuse tri...
 3.6.12: Draw the new position of TEA if it is reflected over the dotted lin...
 3.6.13: Draw each figure and decide how many reflectional and rotational sy...
 3.6.14: Sketch the threedimensional figure formed by folding the net at ri...
 3.6.15: If a polygon has 500 diagonals from each vertex, how many sides doe...
 3.6.16: Use your geometry tools to draw parallelogram CARE so that CA 5.5 c...
Solutions for Chapter 3.6: Construction Problems
Full solutions for Discovering Geometry: An Investigative Approach  4th Edition
ISBN: 9781559538824
Solutions for Chapter 3.6: Construction Problems
Get Full SolutionsDiscovering Geometry: An Investigative Approach was written by and is associated to the ISBN: 9781559538824. Since 16 problems in chapter 3.6: Construction Problems have been answered, more than 19833 students have viewed full stepbystep solutions from this chapter. Chapter 3.6: Construction Problems includes 16 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Discovering Geometry: An Investigative Approach, edition: 4.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.