 62.1: Vocabulary Apply the vocabulary from this lesson to answer each que...
 62.2: Vocabulary Apply the vocabulary from this lesson to answer each que...
 62.3: Safety The handrail is made from congruentparallelograms. In ABCD, ...
 62.4: Safety The handrail is made from congruentparallelograms. In ABCD, ...
 62.5: Safety The handrail is made from congruentparallelograms. In ABCD, ...
 62.6: Safety The handrail is made from congruentparallelograms. In ABCD, ...
 62.7: Safety The handrail is made from congruentparallelograms. In ABCD, ...
 62.8: Safety The handrail is made from congruentparallelograms. In ABCD, ...
 62.9: JKLM is a parallelogram. Find each measure.JK
 62.10: JKLM is a parallelogram. Find each measure.LM
 62.11: JKLM is a parallelogram. Find each measure.mL
 62.12: JKLM is a parallelogram. Find each measure.mM
 62.13: MultiStep Three vertices of DFGH are D (9, 4) , F (1, 5) , and G...
 62.14: Write a twocolumn proof. Given: PSTV is a parallelogram. PQ RQProv...
 62.15: Shipping Cranes can be used to loadcargo onto ships. In JKLM, JL = ...
 62.16: Shipping Cranes can be used to loadcargo onto ships. In JKLM, JL = ...
 62.17: Shipping Cranes can be used to loadcargo onto ships. In JKLM, JL = ...
 62.18: Shipping Cranes can be used to loadcargo onto ships. In JKLM, JL = ...
 62.19: Shipping Cranes can be used to loadcargo onto ships. In JKLM, JL = ...
 62.20: Shipping Cranes can be used to loadcargo onto ships. In JKLM, JL = ...
 62.21: WXYZ is a parallelogram. Find each measure. WV
 62.22: WXYZ is a parallelogram. Find each measure. YW
 62.23: WXYZ is a parallelogram. Find each measure. XZ
 62.24: WXYZ is a parallelogram. Find each measure. ZV
 62.25: MultiStep Three vertices of PRTV are P (4, 4) , R (10, 0) ,and ...
 62.26: Write a twocolumn proof. Given: ABCD and AFGH are parallelograms.P...
 62.27: Algebra The perimeter of PQRS is 84. Find the length of each side o...
 62.28: Algebra The perimeter of PQRS is 84. Find the length of each side o...
 62.29: Algebra The perimeter of PQRS is 84. Find the length of each side o...
 62.30: Algebra The perimeter of PQRS is 84. Find the length of each side o...
 62.31: Cars To repair a large truck, a mechanicmight use a parallelogram l...
 62.32: Complete each statement about KMPR. Justify your answer.MPR ?
 62.33: Complete each statement about KMPR. Justify your answer.PRK ?
 62.34: Complete each statement about KMPR. Justify your answer.MT ?
 62.35: Complete each statement about KMPR. Justify your answer.PR ?
 62.36: Complete each statement about KMPR. Justify your answer.MP ?
 62.37: Complete each statement about KMPR. Justify your answer.MK ?
 62.38: Complete each statement about KMPR. Justify your answer.MPK ?
 62.39: Complete each statement about KMPR. Justify your answer.MTK ?
 62.40: Complete each statement about KMPR. Justify your answer.mMKR + mPRK...
 62.41: Find the values of x, y, and z in each parallelogram.41
 62.42: Find the values of x, y, and z in each parallelogram.42
 62.43: Find the values of x, y, and z in each parallelogram.43
 62.44: Complete the paragraph proof of Theorem 624 by filling in the bla...
 62.45: Write a twocolumn proof of Theorem 623: If a quadrilateral is a ...
 62.46: Algebra Find the values of x and y in each parallelogram.46
 62.47: Algebra Find the values of x and y in each parallelogram.47
 62.48: This problem will prepare you for the Concept Connection on page 40...
 62.49: Critical Thinking Draw any parallelogram. Draw a second parallelogr...
 62.50: Write About It Explain why every parallelogram is a quadrilateral b...
 62.51: What is the value of x in PQRS? 15 30 20 70
 62.52: The diagonals of JKLM intersect at Z. Which statement is true?JL = ...
 62.53: Gridded Response In ABCD, BC = 8.2, and CD = 5. What is the perimet...
 62.54: The coordinates of three vertices of a parallelogram are given. Giv...
 62.55: The coordinates of three vertices of a parallelogram are given. Giv...
 62.56: The feathers on an arrow form two congruent parallelogramsthat shar...
 62.57: Prove that the bisectors of two consecutive anglesof a parallelogra...
 62.58: Describe the correlation shown in each scatter plot as positive, ne...
 62.59: Describe the correlation shown in each scatter plot as positive, ne...
 62.60: Classify each angle pair. (Lesson 31) 2 and 7
 62.61: Classify each angle pair. (Lesson 31) 5 and 4
 62.62: Classify each angle pair. (Lesson 31) 6 and 7
 62.63: Classify each angle pair. (Lesson 31) 1 and 3
 62.64: An interior angle measure of a regular polygon is given. Find the n...
 62.65: An interior angle measure of a regular polygon is given. Find the n...
 62.66: An interior angle measure of a regular polygon is given. Find the n...
Solutions for Chapter 62: Properties of Parallelograms
Full solutions for Geometry  1st Edition
ISBN: 9780030923456
Solutions for Chapter 62: Properties of Parallelograms
Get Full SolutionsGeometry was written by and is associated to the ISBN: 9780030923456. Since 66 problems in chapter 62: Properties of Parallelograms have been answered, more than 42124 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Geometry, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 62: Properties of Parallelograms includes 66 full stepbystep solutions.

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.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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.

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.

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.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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

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.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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).

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.

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

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.