 5.4.1: How many midsegments does a triangle have? A trapezoid have?
 5.4.2: What is the perimeter of TOP?
 5.4.3: x = y =
 5.4.4: z =
 5.4.5: What is the perimeter of TEN ?
 5.4.6: m= n= p=
 5.4.7: q =
 5.4.8: Developing Proof Copy and complete the flowchart to show that LN ...
 5.4.9: Construction When you connected the midpoints of the three sides of...
 5.4.10: Deep in a tropical rain forest, archaeologist Ertha Diggs and her a...
 5.4.11: Ladie and Casey pride themselves on their estimation skills and tak...
 5.4.12: The 40by60by80 cm sealed rectangular container shown at right i...
 5.4.13: Developing Proof Write the converse of this statement: If exactly o...
 5.4.14: Developing Proof Trace the figure below. Calculate the measure of e...
 5.4.15: CART is an isosceles trapezoid. What are the coordinates of point T ?
 5.4.16: HRSE is a kite. What are the coordinates of point R?
 5.4.17: Find the coordinates of midpoints E and Z. Show that the slope of t...
 5.4.18: Construction Use the kite properties you discovered in Lesson 5.3 t...
Solutions for Chapter 5.4: Properties of Midsegments
Full solutions for Discovering Geometry: An Investigative Approach  4th Edition
ISBN: 9781559538824
Solutions for Chapter 5.4: Properties of Midsegments
Get Full SolutionsSince 18 problems in chapter 5.4: Properties of Midsegments have been answered, more than 22419 students have viewed full stepbystep solutions from this chapter. Chapter 5.4: Properties of Midsegments includes 18 full stepbystep solutions. Discovering Geometry: An Investigative Approach was written by and is associated to the ISBN: 9781559538824. 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.

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).

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

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

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 .

Iterative method.
A sequence of steps intended to approach the desired solution.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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

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

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

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

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.