 13.7.1: In Exercises 1 and 2, write a proof and draw the family tree of eac...
 13.7.2: In Exercises 1 and 2, write a proof and draw the family tree of eac...
 13.7.3: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.4: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.5: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.6: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.7: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.8: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.9: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.10: In Exercises 310, write a proof of the conjecture. Once you have co...
 13.7.11: Create a family tree for the Parallel/Proportionality Theorem.
 13.7.12: Create a family tree for the SSS Similarity Theorem.
 13.7.13: Create a family tree for the Pythagorean Theorem.
 13.7.14: A circle with diameter 9.6 cm has two parallel chords with lengths ...
 13.7.15: Choose A if the value is greater in the regular hexagon. Choose B i...
 13.7.16: MiniInvestigation Cut out a small nonsymmetric concave quadrilater...
 13.7.17: Technology Use geometry software to draw a small nonsymmetric conca...
 13.7.18: Given: Circles P and Q PS and PT are tangent to circle Q m SPQ = 57...
 13.7.19: Each arc is a quarter of a circle with its center at a vertex of th...
 13.7.20: Technology The diagram below shows a scalene triangle with angle bi...
 13.7.21: Dakota Davis is at an archaeological dig where he has uncovered a s...
Solutions for Chapter 13.7: Similarity Proofs
Full solutions for Discovering Geometry: An Investigative Approach  4th Edition
ISBN: 9781559538824
Solutions for Chapter 13.7: Similarity Proofs
Get Full SolutionsChapter 13.7: Similarity Proofs includes 21 full stepbystep solutions. This textbook survival guide was created for the textbook: Discovering Geometry: An Investigative Approach, edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Discovering Geometry: An Investigative Approach was written by and is associated to the ISBN: 9781559538824. Since 21 problems in chapter 13.7: Similarity Proofs have been answered, more than 24967 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).