 41.1: Vocabulary Apply the vocabulary from this lesson to answer each que...
 41.2: Vocabulary Apply the vocabulary from this lesson to answer each que...
 41.3: Classify each triangle by its angle measures. DBC
 41.4: Classify each triangle by its angle measures. ABD
 41.5: Classify each triangle by its angle measures. ADC
 41.6: Classify each triangle by its side lengths.EGH
 41.7: Classify each triangle by its side lengths.EFH
 41.8: Classify each triangle by its side lengths.HFG
 41.9: MultiStep Find the side lengths of each triangle.9
 41.10: MultiStep Find the side lengths of each triangle.10
 41.11: Crafts A jeweler creates triangular earrings by bendingpieces of si...
 41.12: Classify each triangle by its angle measures.BEA
 41.13: Classify each triangle by its angle measures.DBC
 41.14: Classify each triangle by its angle measures.ABC
 41.15: Classify each triangle by its side lengths.PST
 41.16: Classify each triangle by its side lengths.RSP
 41.17: Classify each triangle by its side lengths.RPT
 41.18: MultiStep Find the side lengths of each triangle.18
 41.19: MultiStep Find the side lengths of each triangle.19
 41.20: Draw a triangle large enough to measure. Label the vertices X, Y, a...
 41.21: Carpentry Use the following information for Exercises 21 and 22.A m...
 41.22: Carpentry Use the following information for Exercises 21 and 22.A m...
 41.23: Draw an example of each type of triangle or explain why it is not p...
 41.24: Draw an example of each type of triangle or explain why it is not p...
 41.25: Draw an example of each type of triangle or explain why it is not p...
 41.26: Draw an example of each type of triangle or explain why it is not p...
 41.27: Draw an example of each type of triangle or explain why it is not p...
 41.28: Draw an example of each type of triangle or explain why it is not p...
 41.29: An equilateral triangle has a perimeter of 105 in.What is the lengt...
 41.30: Classify each triangle by its angles and sides.ABC
 41.31: Classify each triangle by its angles and sides.ACD
 41.32: An isosceles triangle has a perimeter of 34 cm. The congruent sides...
 41.33: Architecture The base of the Flatiron Building is a triangle border...
 41.34: Critical Thinking Is every isosceles triangle equilateral? Is every...
 41.35: Tell whether each statement is sometimes, always, or never true. Su...
 41.36: Tell whether each statement is sometimes, always, or never true. Su...
 41.37: Tell whether each statement is sometimes, always, or never true. Su...
 41.38: Write About It Write a formula for the side length s of an equilate...
 41.39: Construction Use the method for constructing congruent segments to ...
 41.40: This problem will prepare you for the Concept Connection on page 23...
 41.41: What is the side length of an equilateral triangle with a perimeter...
 41.42: The vertices of RST are R (3, 2), S (2, 3), and T (2, 1). Which o...
 41.43: Which of the following is NOT a correctclassification of LMN? Acute...
 41.44: Gridded Response ABC is isosceles, and AB AC . AB = (__12 x +__14 )...
 41.45: A triangle has vertices with coordinates (0, 0) , (a, 0) , and (0, ...
 41.46: Write a twocolumn proof. Given: ABC is equiangular.EF ACProve: EFB...
 41.47: Two sides of an equilateral triangle measure (y + 10) units and (y ...
 41.48: MultiStep The average length of the sides of PQR is 24. How much l...
 41.49: Name the parent function of each function. (Previous course)y = 5x ...
 41.50: Name the parent function of each function. (Previous course)2y = 3x...
 41.51: Name the parent function of each function. (Previous course)y = 2 (...
 41.52: Determine if each biconditional is true. If false, give a counter e...
 41.53: Determine if each biconditional is true. If false, give a counter e...
 41.54: Determine if each biconditional is true. If false, give a counter e...
 41.55: Determine whether each line is parallel to, is perpendicular to, or...
 41.56: Determine whether each line is parallel to, is perpendicular to, or...
 41.57: Determine whether each line is parallel to, is perpendicular to, or...
 41.58: Determine whether each line is parallel to, is perpendicular to, or...
Solutions for Chapter 41: Classifying Triangles
Full solutions for Geometry  1st Edition
ISBN: 9780030923456
Solutions for Chapter 41: Classifying Triangles
Get Full SolutionsThis textbook survival guide was created for the textbook: Geometry, edition: 1. Chapter 41: Classifying Triangles includes 58 full stepbystep solutions. Geometry was written by and is associated to the ISBN: 9780030923456. Since 58 problems in chapter 41: Classifying Triangles have been answered, more than 44284 students have viewed full stepbystep solutions from this chapter. 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.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

Column space C (A) =
space of all combinations of the columns of A.

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

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

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

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.

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

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.

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).

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

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

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.

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·