 5.3.1: Use your new conjectures to find the missing measures.
 5.3.2: Use your new conjectures to find the missing measures.
 5.3.3: Use your new conjectures to find the missing measures.
 5.3.4: Use your new conjectures to find the missing measures.
 5.3.5: Use your new conjectures to find the missing measures.
 5.3.6: Use your new conjectures to find the missing measures.
 5.3.7: Use your new conjectures to find the missing measures.
 5.3.8: Use your new conjectures to find the missing measures.
 5.3.9: Copy and complete the flowchart to show how the Kite Angle Bisector...
 5.3.10: Write a paragraph proof or flowchart proof of the Kite Diagonal Bis...
 5.3.11: Sketch and label kite KITE with vertex angles K and T and KI > TE. ...
 5.3.12: Sketch and label trapezoid QUIZ with one base QU . What is the othe...
 5.3.13: Sketch and label isosceles trapezoid SHOW with one base SH . What i...
 5.3.14: In Exercises 1416, use the properties of kites and trapezoids to co...
 5.3.15: In Exercises 1416, use the properties of kites and trapezoids to co...
 5.3.16: In Exercises 1416, use the properties of kites and trapezoids to co...
 5.3.17: Application The inner edge of the arch in the diagram above right i...
 5.3.18: The figure below shows the path of light through a trapezoidal pris...
 5.3.19: Developing Proof Trace the figure below. Calculate the measure of e...
Solutions for Chapter 5.3: Kite and Trapezoid Properties
Full solutions for Discovering Geometry: An Investigative Approach  4th Edition
ISBN: 9781559538824
Solutions for Chapter 5.3: Kite and Trapezoid Properties
Get Full SolutionsSince 19 problems in chapter 5.3: Kite and Trapezoid Properties have been answered, more than 24649 students have viewed full stepbystep solutions from this chapter. Chapter 5.3: Kite and Trapezoid Properties includes 19 full stepbystep solutions. This textbook survival guide was created for the textbook: Discovering Geometry: An Investigative Approach, edition: 4. Discovering Geometry: An Investigative Approach was written by and is associated to the ISBN: 9781559538824. This expansive textbook survival guide covers the following chapters and their solutions.

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

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

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

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

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.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.