- 6-6.1: Vocabulary Apply the vocabulary from this lesson to answer each que...
- 6-6.2: Vocabulary Apply the vocabulary from this lesson to answer each que...
- 6-6.3: Crafts The edges of the kite-shaped glass inthe sun catcher are sea...
- 6-6.4: In kite WXYZ, mWXY = 104,and mVYZ = 49.Find each measure.mVZY
- 6-6.5: In kite WXYZ, mWXY = 104,and mVYZ = 49.Find each measure.mVXW
- 6-6.6: In kite WXYZ, mWXY = 104,and mVYZ = 49.Find each measure.mXWZ
- 6-6.7: Find mA.
- 6-6.8: RW = 17.7, and SV = 23.3. Find TW
- 6-6.9: Find the value of z so that EFGH is isosceles.
- 6-6.10: MQ = 7y - 6, and LP = 4y + 11.Find the value of y so thatLMPQ is is...
- 6-6.11: Find QR
- 6-6.12: Find AZ
- 6-6.13: Design Each square section in the iron railing contains four small ...
- 6-6.14: In kite ABCD, mDAX = 32, and mXDC = 64. Find each measure.mXDA
- 6-6.15: In kite ABCD, mDAX = 32, and mXDC = 64. Find each measure.mABC
- 6-6.16: In kite ABCD, mDAX = 32, and mXDC = 64. Find each measure.mBCD
- 6-6.17: Find mQ.
- 6-6.18: SZ = 62.6, and KZ = 34. Find RJ.
- 6-6.19: Algebra Find the value of a so that XYZW is isosceles. Give your an...
- 6-6.20: Algebra GJ = 4x - 1, and FH = 9x - 15. Find the value of x so that ...
- 6-6.21: Find PQ.
- 6-6.22: Find KR.
- 6-6.23: Tell whether each statement is sometimes, always, or never true.The...
- 6-6.24: Tell whether each statement is sometimes, always, or never true.The...
- 6-6.25: Tell whether each statement is sometimes, always, or never true.A p...
- 6-6.26: Estimation Hal is building a trapezoid-shapedframe for a flower bed...
- 6-6.27: Find the measure of each numbered angle.27
- 6-6.28: Find the measure of each numbered angle.28
- 6-6.29: Find the measure of each numbered angle.29
- 6-6.30: Find the measure of each numbered angle.30
- 6-6.31: Find the measure of each numbered angle.31
- 6-6.32: Find the measure of each numbered angle.32
- 6-6.33: This problem will prepare you for the Concept Connection on page 43...
- 6-6.34: Algebra Find the length of the midsegment of each trapezoid34
- 6-6.35: Algebra Find the length of the midsegment of each trapezoid35
- 6-6.36: Algebra Find the length of the midsegment of each trapezoid36
- 6-6.37: Mechanics A Peaucellier cell is made of seven rods connected by joi...
- 6-6.38: Prove that one diagonal of a kite bisects a pair ofopposite angles ...
- 6-6.39: Prove Theorem 6-6-1: If a quadrilateral is a kite,then its diagonal...
- 6-6.40: Multi-Step Give the best name for a quadrilateral with the given ve...
- 6-6.41: Multi-Step Give the best name for a quadrilateral with the given ve...
- 6-6.42: Multi-Step Give the best name for a quadrilateral with the given ve...
- 6-6.43: Multi-Step Give the best name for a quadrilateral with the given ve...
- 6-6.44: Carpentry The window frame is a regular octagon.It is made from eig...
- 6-6.45: Write About It Compare an isosceles trapezoid to atrapezoid that is...
- 6-6.46: Use coordinates to verify the Trapezoid Midsegment Theorem. a. M is...
- 6-6.47: In trapezoid PQRS, what could be the lengths of QR and PS ? 6 and 1...
- 6-6.48: Which statement is never true for a kite? The diagonals are perpend...
- 6-6.49: Gridded Response What is the length of the midsegment of trapezoid ...
- 6-6.50: Write a two-column proof. (Hint: If there is a line and a point not...
- 6-6.51: The perimeter of isosceles trapezoid ABCD is 27.4 inches. If BC = 2...
- 6-6.52: An empty pool is being filled with water. After 10 hours, 20% of th...
- 6-6.53: Write and solve an inequality for x. (Lesson 3-4)53
- 6-6.54: Write and solve an inequality for x. (Lesson 3-4)54
- 6-6.55: Tell whether a parallelogram with the given vertices is a rectangle...
- 6-6.56: Tell whether a parallelogram with the given vertices is a rectangle...
Solutions for Chapter 6-6: Properties of Kites and Trapezoids
Full solutions for Geometry | 1st Edition
Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).
Remove row i and column j; multiply the determinant by (-I)i + j •
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 n-l - An).
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.
Diagonal matrix D.
dij = 0 if i #- j. Block-diagonal: zero outside square blocks Du.
Hilbert matrix hilb(n).
Entries HU = 1/(i + j -1) = Jd X i- 1 xj-1dx. Positive definite but extremely small Amin and large condition number: H is ill-conditioned.
Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.
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.
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.
Every v in V is orthogonal to every w in W.
Outer product uv T
= column times row = rank one matrix.
Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.
Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.
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.
Schur complement S, D - C A -} B.
Appears in block elimination on [~ g ].
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!
Singular matrix A.
A square matrix that has no inverse: det(A) = o.
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.
Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn- 1 with P(Xi) = bi. Vij = (Xi)j-I and det V = product of (Xk - Xi) for k > i.