 54.1: Vocabulary The midsegment of a triangle joins the ? of two sides of...
 54.2: The vertices of PQR are P (4, 1) , Q (2, 9) , and R (6, 3) . S is...
 54.3: Find each measure. NM
 54.4: Find each measure. XZ
 54.5: Find each measure. NZ
 54.6: Find each measure. mLMN
 54.7: Find each measure. mYXZ
 54.8: Find each measure. mXLM
 54.9: Architecture In this Aframe house,the width of the first floor XZ ...
 54.10: The vertices of ABC are A (6, 11) , B (6, 3) , and C (2, 5) . D...
 54.11: Find each measure.GJ
 54.12: Find each measure.RQ
 54.13: Find each measure.RJ
 54.14: Find each measure.mPQR
 54.15: Find each measure.mHGJ
 54.16: Find each measure.mGPQ
 54.17: Carpentry In each support for the garden swing,the crossbar DE is a...
 54.18: KLM is the midsegment triangle of GHJ. What is the perimeter of GHJ?
 54.19: KLM is the midsegment triangle of GHJ. What is the perimeter of KLM?
 54.20: KLM is the midsegment triangle of GHJ. What is the relationship bet...
 54.21: Algebra Find the value of n in each triangle21
 54.22: Algebra Find the value of n in each triangle22
 54.23: Algebra Find the value of n in each triangle23
 54.24: Algebra Find the value of n in each triangle24
 54.25: Algebra Find the value of n in each triangle25
 54.26: Algebra Find the value of n in each triangle26
 54.27: /////ERROR ANALYSIS///// Below are two solutions for finding BC. Wh...
 54.28: Critical Thinking Draw scalene DEF. Label X as the midpoint of DE ,...
 54.29: Estimation The diagram shows the sketch for a new street. Parallel ...
 54.30: CG ,EH , and FJ are midsegments of ABD, GCD, and GHE, respectively....
 54.31: CG ,EH , and FJ are midsegments of ABD, GCD, and GHE, respectively....
 54.32: CG ,EH , and FJ are midsegments of ABD, GCD, and GHE, respectively....
 54.33: CG ,EH , and FJ are midsegments of ABD, GCD, and GHE, respectively....
 54.34: CG ,EH , and FJ are midsegments of ABD, GCD, and GHE, respectively....
 54.35: CG ,EH , and FJ are midsegments of ABD, GCD, and GHE, respectively....
 54.36: Write About It An isosceles triangle hastwo congruent sides. Does i...
 54.37: This problem will prepare you for the Concept Connection on page 32...
 54.38: Use coordinates to prove the Triangle Midsegment Theorem. a. M is t...
 54.39: PQ is a midsegment of RST. What is the length of RT ? 9 meters 21 m...
 54.40: In UVW, M is the midpoint of VU , and N is themidpoint of VW . Whic...
 54.41: XYZ is the midsegment triangle of JKL, XY = 8, YK = 14, and mYKZ = ...
 54.42: MultiStep The midpoints of the sides of a triangle are A (6, 3) ,...
 54.43: . Critical Thinking Classify the midsegment triangle of an equilate...
 54.44: Algebra Find the value of n in each triangle.44
 54.45: Algebra Find the value of n in each triangle.45
 54.46: XYZ is the midsegment triangle of PQR. Write a congruence statement...
 54.47: AB is a midsegment of XYZ.CD is a midsegment of ABZ. EFis a midsegm...
 54.48: Suppose a 2% acid solution is mixed with a 3% acid solution. Find t...
 54.49: Suppose a 2% acid solution is mixed with a 3% acid solution. Find t...
 54.50: A figure has vertices G (3, 2) , H (0, 0) , J (4, 1) , and K (1, ...
 54.51: A figure has vertices G (3, 2) , H (0, 0) , J (4, 1) , and K (1, ...
 54.52: A figure has vertices G (3, 2) , H (0, 0) , J (4, 1) , and K (1, ...
 54.53: Find each length. (Lesson 53) NX
 54.54: Find each length. (Lesson 53) MR
 54.55: Find each length. (Lesson 53) NP
Solutions for Chapter 54: The Triangle Midsegment Theorem
Full solutions for Geometry  1st Edition
ISBN: 9780030923456
Solutions for Chapter 54: The Triangle Midsegment Theorem
Get Full SolutionsChapter 54: The Triangle Midsegment Theorem includes 55 full stepbystep solutions. Since 55 problems in chapter 54: The Triangle Midsegment Theorem have been answered, more than 42286 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Geometry, edition: 1. Geometry was written by and is associated to the ISBN: 9780030923456. This expansive textbook survival guide covers the following chapters and their solutions.

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

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

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

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

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

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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.

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = 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).

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

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.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Solvable system Ax = b.
The right side b is in the column space of A.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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.