1. Explain why AC is the perpendicular bisector of BD. AD; BC = DC; PR = QS,;...
Fantastic news! We've Found the answer you've been seeking!
Question:
1. Explain why AC is the perpendicular bisector of BD.
Transcribed Image Text:
AD; BC = DC; PR = QS,; P, Q, R, and S are the midpoints of AB, BC, DC, and AD respectively, Questions 2-5: Statements in a proof are provided. Write the reason that best justifies each statement. 1) Explain why AC is the perpendicular bisector of BD. Statements Reasons AB = AD; BC = DC; PR s QS; P, Q, R, and S are the midpoints of AB, BC, DC, and AD respectively. Given 2) PQ || AC; SR || AC: PS || BD; QR | BD 2 lA aplane, 2 lines t to th suo ime. 3) PQ |I| SR; PS I| QR 3) Transative Property 4) PQRS is a parallelogram. 4) Def. of paralelogram 5) PQRS is a rectangle. The diagonals of a vectangi 5) A 全 For the Questions 6-8, let AB = 10, BC = 8, B0 = 6, and AO = 8 6) Find the length of PS. 7) M and N are the midpoints of PB and SD respectively. Find MN. 4 8) *Let MLPBD = x2 + 4 and mzPSD = 4x + 99. If x > 0, find mzSDB. For questions 9-12, consider quadrilateral ASOP. - Note that it can be proven that AAFP = AAFS by the hypotenuse-leg theorem for triangle congruence. - Since corresponding parts of congruent triangles are congruent, PF = FS. 9) Explain why AF = OF. 10) Why is ASOP a parallelogram? 11) Why is ASOP a rhombus? 2) *Let mLSOP = 74°, mLPAF = 2j +k, and mzSFO = 5j + k. Solve for the values of j and k. Questions 8 & 12, the expressions represent the measures of the stated angles to the nearest degree. AD; BC = DC; PR = QS,; P, Q, R, and S are the midpoints of AB, BC, DC, and AD respectively, Questions 2-5: Statements in a proof are provided. Write the reason that best justifies each statement. 1) Explain why AC is the perpendicular bisector of BD. Statements Reasons AB = AD; BC = DC; PR s QS; P, Q, R, and S are the midpoints of AB, BC, DC, and AD respectively. Given 2) PQ || AC; SR || AC: PS || BD; QR | BD 2 lA aplane, 2 lines t to th suo ime. 3) PQ |I| SR; PS I| QR 3) Transative Property 4) PQRS is a parallelogram. 4) Def. of paralelogram 5) PQRS is a rectangle. The diagonals of a vectangi 5) A 全 For the Questions 6-8, let AB = 10, BC = 8, B0 = 6, and AO = 8 6) Find the length of PS. 7) M and N are the midpoints of PB and SD respectively. Find MN. 4 8) *Let MLPBD = x2 + 4 and mzPSD = 4x + 99. If x > 0, find mzSDB. For questions 9-12, consider quadrilateral ASOP. - Note that it can be proven that AAFP = AAFS by the hypotenuse-leg theorem for triangle congruence. - Since corresponding parts of congruent triangles are congruent, PF = FS. 9) Explain why AF = OF. 10) Why is ASOP a parallelogram? 11) Why is ASOP a rhombus? 2) *Let mLSOP = 74°, mLPAF = 2j +k, and mzSFO = 5j + k. Solve for the values of j and k. Questions 8 & 12, the expressions represent the measures of the stated angles to the nearest degree.
Expert Answer:
Answer rating: 100% (QA)
Q1 Statement Reason 1 AB AD and BC DC Given 2 ABCD is a kite Properties of kite ie 2 pairs of equallength sides and these sides are adjacent to each o... View the full answer
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
Students also viewed these mathematics questions
-
Let A = {R, S| R and S are regular expressions and L(R) L(S)}. Show that A is decidable.
-
Let EQ REX = {R, S| R and S are equivalent regular expressions}. Show that EQ REX PSPACE.
-
Explain how R and S are related to and (+) (-).
-
The statement of financial position of Kingbird Limited follows for the current year, 2020: KINGBIRD LIMITED Statement of Financial Position December 31, 2020 Current assets $135,660 Current...
-
Mass spectrometry is more often applied to molecules than to atoms. We will see in Chapter 3 that the molecular weight of a molecule is the sum of the atomic weights of the atoms in the molecule. The...
-
A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 100 units per week. The weekly fixed cost of keeping each warehouse...
-
Provide examples for sequential access, both real and virtual.
-
Hertz Corporation is incorporated in the state of Delaware and has its headquarters in the state of New Jersey. Melinda Friend, a California citizen, sued the Hertz Corporation in California state...
-
Marion no longer needs a large house and has decided to sell the property and to purchase a townhouse. The expected proceeds from the sale of the large house is AUD2.5 million. From these proceeds,...
-
The focus of this project is to create a master budget for the Williams Company based on the companys industry outlook, recent company outcomes, and the companys business rules. You will create a...
-
3) How are the compounds in each pair related to each other? Are they identical, enantiomers, diastereomers or constitutional isomers? CI, H CI H CI H and and H OH HO H H CI CI H OH CI HO CI and...
-
Portfolios are a comprehensive approach to reporting overall student growth. How can educators utilize various assessment methods such as checklists, rating scales, and authentic assessment to build...
-
1. In the October 17, 2020 Minutes of the Audit Committee, Mr. Ramirez, Apollo's internal auditor, stated that the year before, the company had been able to save on audit fees when their staff had...
-
There are four errors in the following code. List the line numbers with errors and briefly state the problem for each: 1 // NOTE: There are errors in the following code 2 public 1234567 8 9 10 11 12...
-
Provide a brief explanation as to why you believe there are some differences between the two sets of rates (AA nonfinancial vs. AA financial)
-
You save $100 and earn 7% (annual) interest. How much will you have total after two years assuming you reinvest principal and interest
-
Romeo and Juliet is a timeless tragedy that has captured the hearts of imaginations and audiences for centuries. William Shakespeare's play follows a love story of two young lovers in feuding...
-
Pappa's Appliances uses the periodic inventory system. Details regarding the inventory of appliances at January 1, purchases invoices during the year, and the inventory count at December 31 are...
-
Let (B, +, , , 0, 1) be a Boolean algebra that is partially ordered by . If w, x, y, z B with w x and y z, prove that (a) wy xy; and (b) w + y x + z.
-
Let G = (V, E) be bipartite with V partitioned as X Y. For all x X, deg(x) > 3, and for all y Y, deg(y) < 7. If |X| < 50, find an upper bound (that is as small as possible) on (G).
-
Let n ¥ 2. If xl is a Boolean variable for all 1 ¤ i ¤ n, prove that (X + x ++ x,) = x, I,
-
Use Eqs. (7.27)-(7.31) to verify the entries in Table 7.1. Data from Eq. 7.27 Data from Eq. 7.28 Data from Eq. 7.29 Data from Eq. 7.30 Data from Eq. 7.31 Data from Table 7.1 n = 2 a.m = q- p.
-
Use the definition of the adjoint representation matrices (3.8), to compute the action of a generator \(X_{a}\) on a state \(\left|X_{b} ightangle\) given in Eq. (7.3). Data from Eq. 3.8 Data from...
-
Show that the operators given in Eq. (7.20) have the SU(2) commutators (7.21). Data from Eq. (7.20) Data from Eq. (7.21) Eta a. H E = E3 E = |a| a
Study smarter with the SolutionInn App