 43.1: Vocabulary Apply the vocabulary from this lesson to answer each que...
 43.2: Vocabulary Apply the vocabulary from this lesson to answer each que...
 43.3: Given: RST LMN. Identify the congruent corresponding parts.RS ?
 43.4: Given: RST LMN. Identify the congruent corresponding parts.LN ?
 43.5: Given: RST LMN. Identify the congruent corresponding parts.S ?
 43.6: Given: RST LMN. Identify the congruent corresponding parts.TS ?
 43.7: Given: RST LMN. Identify the congruent corresponding parts.L ?
 43.8: Given: RST LMN. Identify the congruent corresponding parts.N ?
 43.9: Given: FGH JKL. Find each value. KL
 43.10: Given: FGH JKL. Find each value. x
 43.11: Given: E is the midpoint of AC and BD .AB CD , AB CD Prove: ABE CDE...
 43.12: Engineering The geodesic domeshown is a 14story building thatmodel...
 43.13: Given: Polygon CDEF polygon KLMN. Identify the congruent correspond...
 43.14: Given: Polygon CDEF polygon KLMN. Identify the congruent correspond...
 43.15: Given: Polygon CDEF polygon KLMN. Identify the congruent correspond...
 43.16: Given: Polygon CDEF polygon KLMN. Identify the congruent correspond...
 43.17: Given: ABD CBD. Find each value. mC
 43.18: Given: ABD CBD. Find each value. y
 43.19: Given: MP bisects NMR. P is the midpoint of NR . MN MR , N RProve: ...
 43.20: Hobbies In a garden, triangular flower Abeds are separated by strai...
 43.21: For two triangles, the followingcorresponding parts are given:GS KP...
 43.22: The two polygons in the diagram are congruent.Complete the followin...
 43.23: Write and solve an equation for each of the following.ABC DEF. AB =...
 43.24: Write and solve an equation for each of the following.JKL MNP. mL =...
 43.25: Write and solve an equation for each of the following.Polygon ABCD ...
 43.26: This problem will prepare you for the Concept Connection on page 23...
 43.27: Draw a diagram and then write a proof.Given:BD AC . D is the midpoi...
 43.28: Critical Thinking Draw two triangles that are not congruent but hav...
 43.29: /////ERROR ANALYSIS///// Given MPQ EDF.Two solutions for finding mE...
 43.30: . Write About It Given the diagram of the triangles, is there enoug...
 43.31: Which congruence statement correctly indicates that the two given t...
 43.32: MNP RST. What are the values of x and y?x = 26, y = 21 _13 x = 25, ...
 43.33: ABC XYZ. mA = 47.1, and mC = 13.8. Find mY. 13.8 76.2 42.9 119.1
 43.34: MNR SPQ, NL = 18, SP = 33, SR = 10, RQ = 24, and QP = 30. What is t...
 43.35: MultiStep Given that the perimeter of TUVW is 149 units, find the ...
 43.36: MultiStep Polygon ABCD polygon EFGH. A is a right angle.mE = (y 2 ...
 43.37: Given:RS RT , S TProve: RST RTS
 43.38: Two number cubes are rolled. Find the probability of each outcome.(...
 43.39: Two number cubes are rolled. Find the probability of each outcome.(...
 43.40: Classify each angle by its measure. (Lesson 13)mDOC = 40
 43.41: Classify each angle by its measure. (Lesson 13)mBOA = 90
 43.42: Classify each angle by its measure. (Lesson 13)mCOA = 140
 43.43: Find each angle measure. (Lesson 42) Q
 43.44: Find each angle measure. (Lesson 42) P
 43.45: Find each angle measure. (Lesson 42) QRS
Solutions for Chapter 43: Congruent Triangles
Full solutions for Geometry  1st Edition
ISBN: 9780030923456
Solutions for Chapter 43: Congruent Triangles
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 45 problems in chapter 43: Congruent Triangles have been answered, more than 47218 students have viewed full stepbystep solutions from this chapter. Chapter 43: Congruent Triangles includes 45 full stepbystep solutions. Geometry was written by and is associated to the ISBN: 9780030923456. This textbook survival guide was created for the textbook: Geometry, edition: 1.

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.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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.

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.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.