 75.1: Vocabulary Finding distances using similar triangles is called ? .(...
 75.2: Measurement To find the height of a dinosaur ina museum, Amir place...
 75.3: The scale of this blueprint of an art gallery is 1 in. : 48 ft.Find...
 75.4: The scale of this blueprint of an art gallery is 1 in. : 48 ft.Find...
 75.5: The scale of this blueprint of an art gallery is 1 in. : 48 ft.Find...
 75.6: The scale of this blueprint of an art gallery is 1 in. : 48 ft.Find...
 75.7: MultiStep A rectangular classroom is 10 m long and 4.6 m wide.Make...
 75.8: MultiStep A rectangular classroom is 10 m long and 4.6 m wide.Make...
 75.9: MultiStep A rectangular classroom is 10 m long and 4.6 m wide.Make...
 75.10: Given: rectangle MNPQ rectangle RSTUFind the perimeter ofrectangle ...
 75.11: Given: rectangle MNPQ rectangle RSTUFind the area of rectangle RSTU.
 75.12: Measurement Jenny is 5 ft 2 in. tall. To find the height ofa light ...
 75.13: Space Exploration Use the followinginformation for Exercises 13 and...
 75.14: Space Exploration Use the followinginformation for Exercises 13 and...
 75.15: MultiStep A park at the end of a city block is a right triangle wi...
 75.16: MultiStep A park at the end of a city block is a right triangle wi...
 75.17: MultiStep A park at the end of a city block is a right triangle wi...
 75.18: Given that pentagon ABCDE pentagon FGHJK, find each of the followin...
 75.19: Given that pentagon ABCDE pentagon FGHJK, find each of the followin...
 75.20: Estimation Use the scale on the map forExercises 2023. Give the app...
 75.21: Estimation Use the scale on the map forExercises 2023. Give the app...
 75.22: Estimation Use the scale on the map forExercises 2023. Give the app...
 75.23: Estimation Use the scale on the map forExercises 2023. Give the app...
 75.24: Given: ABC DEF The ratio of the perimeter of ABC to the perimeter o...
 75.25: Given: ABC DEF The ratio of the area of ABC to the area of DEF is _...
 75.26: Given: ABC DEF The ratio of the area of ABC to the area of DEF is _...
 75.27: Space Exploration The scale of this model of the space shuttle is1 ...
 75.28: Given that PQR WXY, find each ratio. a. __perimeter of PQRperimeter...
 75.29: Given that rectangle ABCD EFGH . The area of rectangle ABCD is 135 ...
 75.30: Sports An NBA basketball court is 94 ft long and 50 ft wide. Make a...
 75.31: This problem will prepare you for the Concept Connection on page 50...
 75.32: Estimation The photo showsa person who is 5 ft 1 in. tallstanding b...
 75.33: Math History In A.D. 1076,the mathematician Shen Kuawas asked by th...
 75.34: Points X, Y, and Z are the midpoints of JK , KL , and LJ ,respectiv...
 75.35: Critical Thinking Keisha is making two scale drawings of her school...
 75.36: The ratio of the perimeter of square ABCD to the perimeter of squar...
 75.37: Write About It Explain what it would meanto make a scale drawing wi...
 75.38: Write About It One square has twice the area of another square. Exp...
 75.39: ABC RST, and the area of ABC is 24 m 2.What is the area of RST ? 16...
 75.40: A blueprint for a museum uses a scale of __14 in. : 1 ft.One of the...
 75.41: The similarity ratio of two similar pentagons is __94 . What is the...
 75.42: ft 2, find the area of the second. 4 ft 2 8 ft 2 16 ft 2 32 ft 2
 75.43: Astronomy The city of Eugene, Oregon, has ascale model of the solar...
 75.44: Given: ABC DEFProve:AB + BC + AC __ DE + EF +DF =_ABDE
 75.45: Given: PQR WXY Prove:__Area PQR Area WXY = PR _2WY 2
 75.46: Quadrilateral PQRS has side lengths of 6 m, 7 m, 10 m, and 12 m.The...
 75.47: Solve each equation. Round to the nearest hundredth if necessary. (...
 75.48: Solve each equation. Round to the nearest hundredth if necessary. (...
 75.49: Solve each equation. Round to the nearest hundredth if necessary. (...
 75.50: Show that the quadrilateral with the given vertices is a parallelog...
 75.51: Show that the quadrilateral with the given vertices is a parallelog...
 75.52: Given that 58x = 26y, find the ratio y : x in simplest form. (Lesso...
Solutions for Chapter 75: Using Proportional Relationships
Full solutions for Geometry  1st Edition
ISBN: 9780030923456
Solutions for Chapter 75: Using Proportional Relationships
Get Full SolutionsChapter 75: Using Proportional Relationships includes 52 full stepbystep solutions. This textbook survival guide was created for the textbook: Geometry, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 52 problems in chapter 75: Using Proportional Relationships have been answered, more than 42105 students have viewed full stepbystep solutions from this chapter. Geometry was written by and is associated to the ISBN: 9780030923456.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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

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

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).

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

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.

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 .

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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

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

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

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!

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

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.