 53.1: Vocabulary Apply the vocabulary from this lesson to answer each que...
 53.2: Vocabulary Apply the vocabulary from this lesson to answer each que...
 53.3: VX = 204, and RW = 104. Find each length. VW
 53.4: VX = 204, and RW = 104. Find each length. WX
 53.5: VX = 204, and RW = 104. Find each length. RY
 53.6: VX = 204, and RW = 104. Find each length. WY
 53.7: Design The diagram shows a plan for a piece of a mobile. A chain wi...
 53.8: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.9: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.10: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.11: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.12: PA = 2.9, and HC = 10.8. Find each length. PC
 53.13: PA = 2.9, and HC = 10.8. Find each length. HP
 53.14: PA = 2.9, and HC = 10.8. Find each length. JA
 53.15: PA = 2.9, and HC = 10.8. Find each length. JP
 53.16: Design In the plan for a table, the triangular top has coordinates ...
 53.17: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.18: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.19: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.20: MultiStep Find the orthocenter of a triangle with the given vertic...
 53.21: Find each measureGL
 53.22: Find each measurePL
 53.23: Find each measureHL
 53.24: Find each measureGJ
 53.25: Find each measureperimeter of GHJ
 53.26: Find each measurearea of GHJ
 53.27: Algebra Find the centroid of a triangle with the given vertices.A (...
 53.28: Algebra Find the centroid of a triangle with the given vertices.X (...
 53.29: Find each lengthPZ
 53.30: Find each lengthPX
 53.31: Find each lengthQZ
 53.32: Find each lengthYZ
 53.33: Critical Thinking Draw an isosceles triangle and its line of symmet...
 53.34: Tell whether each statement is sometimes, always, or never true. Su...
 53.35: Tell whether each statement is sometimes, always, or never true. Su...
 53.36: Tell whether each statement is sometimes, always, or never true. Su...
 53.37: Tell whether each statement is sometimes, always, or never true. Su...
 53.38: Write a twocolumn proof. Given:PS and RT are medians of PQR. PS RT...
 53.39: Write About It Draw a large triangle on a sheet of paper and cut it...
 53.40: This problem will prepare you for the Concept Connection on page 32...
 53.41: QT , RV , and SW are medians of QRS. Which statement is NOT necessa...
 53.42: Suppose that the orthocenter of a triangle lies outside thetriangle...
 53.43: In the diagram, which of the following correctlydescribes LN ? Alti...
 53.44: Draw an equilateral triangle. a. Explain why the perpendicular bise...
 53.45: Use coordinates to show that the lines containingthe altitudes of a...
 53.46: At a baseball game, a bag of peanuts costs $0.75 more than a bag of...
 53.47: Determine if each biconditional is true. If false, give a counterex...
 53.48: Determine if each biconditional is true. If false, give a counterex...
 53.49: NQ ,QP , and QM are perpendicular bisectors of JKL. Find each measu...
 53.50: NQ ,QP , and QM are perpendicular bisectors of JKL. Find each measu...
 53.51: NQ ,QP , and QM are perpendicular bisectors of JKL. Find each measu...
Solutions for Chapter 53: Medians and Altitudes of Triangles
Full solutions for Geometry  1st Edition
ISBN: 9780030923456
Solutions for Chapter 53: Medians and Altitudes of Triangles
Get Full SolutionsGeometry was written by and is associated to the ISBN: 9780030923456. This textbook survival guide was created for the textbook: Geometry, edition: 1. Chapter 53: Medians and Altitudes of Triangles includes 51 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 51 problems in chapter 53: Medians and Altitudes of Triangles have been answered, more than 44018 students have viewed full stepbystep solutions from this chapter.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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

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

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

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.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

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