 106.1: Determine whether each pair of triangles is similar. Justify your a...
 106.2: Determine whether each pair of triangles is similar. Justify your a...
 106.3: For each set of measures given, find the measures of the missing si...
 106.4: For each set of measures given, find the measures of the missing si...
 106.5: For each set of measures given, find the measures of the missing si...
 106.6: For each set of measures given, find the measures of the missing si...
 106.7: SHADOWS A 25foot flagpole casts a shadow that is 10 feet long and ...
 106.8: Determine whether each pair of triangles is similar. Justify your a...
 106.9: Determine whether each pair of triangles is similar. Justify your a...
 106.10: Determine whether each pair of triangles is similar. Justify your a...
 106.11: Determine whether each pair of triangles is similar. Justify your a...
 106.12: Determine whether each pair of triangles is similar. Justify your a...
 106.13: Determine whether each pair of triangles is similar. Justify your a...
 106.14: For each set of measures given, find the measures of the missing si...
 106.15: For each set of measures given, find the measures of the missing si...
 106.16: For each set of measures given, find the measures of the missing si...
 106.17: For each set of measures given, find the measures of the missing si...
 106.18: For each set of measures given, find the measures of the missing si...
 106.19: For each set of measures given, find the measures of the missing si...
 106.20: For each set of measures given, find the measures of the missing si...
 106.21: For each set of measures given, find the measures of the missing si...
 106.22: PHOTOGRAPHY Refer to the diagram of a camera at the beginning of th...
 106.23: TOYS Diecast model cars use a scale of 1 inch : 2 feet of the real ...
 106.24: GOLF Jessica is playing miniature golf on a hole like the one shown...
 106.25: CRAFTS Melinda is working on a quilt pattern containing isosceles t...
 106.26: MIRRORS For Exercises 26 and 27, use the diagram and the following ...
 106.27: MIRRORS For Exercises 26 and 27, use the diagram and the following ...
 106.28: OPEN ENDED Draw and label a triangle ABC. Then draw and label a sim...
 106.29: REASONING Determine whether the following statement is sometimes, a...
 106.30: FIND THE ERROR Russell and Consuela are comparing the similar trian...
 106.31: CRITICAL THINKING For Exercises 3133, use the following information...
 106.32: CRITICAL THINKING For Exercises 3133, use the following information...
 106.33: CRITICAL THINKING For Exercises 3133, use the following information...
 106.34: Writing in Math Use the information about photography on page 560 t...
 106.35: Which is a true statement about the figure? A ABC ADC B ABC ACD C A...
 106.36: REVIEW Kareem needs to know the length and width of his room but do...
 106.37: Find the distance between each pair of points whose coordinates are...
 106.38: Find the distance between each pair of points whose coordinates are...
 106.39: Find the distance between each pair of points whose coordinates are...
 106.40: The lengths of three sides of a triangle are given. Determine wheth...
 106.41: The lengths of three sides of a triangle are given. Determine wheth...
 106.42: The lengths of three sides of a triangle are given. Determine wheth...
 106.43: Use elimination to solve each system of equations. 2x + y = 4
 106.44: Use elimination to solve each system of equations. 3x  2y = 13
 106.45: Use elimination to solve each system of equations. _1 3 x + _1 2
 106.46: AVIATION An airplane passing over Sacramento at an elevation of 37,...
Solutions for Chapter 106: Similar Triangles
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 106: Similar Triangles
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. Since 46 problems in chapter 106: Similar Triangles have been answered, more than 35424 students have viewed full stepbystep solutions from this chapter. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Chapter 106: Similar Triangles includes 46 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

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].

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.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

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.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.