Videos
a.
To Find: Whether the statement is always true, if sometime is true or never true?
a.
Answer to Problem 19RP
The given statement is always true, hence this statement is written as A
Explanation of Solution
Given:
If the diagonals of a quadrilateral are congruent, the quadrilateral is an isosceles trapezoid.
Concept Used:
An isosceles trapezoid is a convex quadrilateral having a line of symmetry bisecting one pair of opposite sides.
Calculation:
If the diagonals of a quadrilateral are congruent, the quadrilateral is an isosceles trapezoid. This statement is always true, hence this statement is written as A
Conclusion:
The given statement is always true, hence this statement is written as A
b.
To Find: Whether the statement is always true, if sometime is true or never true?
b.
Answer to Problem 19RP
The given statement is always true, hence this statement is written as A
Explanation of Solution
Given:
If the diagonals of a quadrilateral divide each angle into two 45 degrees
Concept Used:
Square is a quadrilateral whose all sides and all angles are of equal measure. Also diagonal divides the angles at each corner into 45 degrees.
Calculation:
If the diagonals of a quadrilateral divide each angle into two 45 degrees angles, the quadrilateral is a square. This statement is always true, hence this statement is written as A
Conclusion:
The given statement is always true, hence this statement is written as A
c.
To Find: Whether the statement is always true, if sometime is true or never true?
c.
Answer to Problem 19RP
The given statement is sometime true, hence this statement is written as S.
Explanation of Solution
Given:
If a parallelogram is equilateral, it is equiangular.
Concept Used:
Equilateral parallelogram is a parallelogram of which all sides are equal. Rhombus is of this category but it is not equiangular, while square is equilateral parallelogram which is equiangular also.
Calculation:
If a parallelogram is equilateral, it is equiangular. This statement is sometimes true, since Rhombus is of this category but it is not equiangular, while square is equilateral parallelogram which is equiangular also. Hence this statement is written as S.
Conclusion:
The given statement is sometime true, hence this statement is written as S.
d.
To Find: Whether the statement is always true, if sometime is true or never true?
d.
Answer to Problem 19RP
The given statement is always true, hence this statement is written as A.
Explanation of Solution
Given:
If two of the angles of a trapezoid are congruent, the trapezoid is isosceles.
Concept Used:
A trapezoid is a quadrilateral with exactly one pair of parallel sides. An isosceles trapezoid is a convex quadrilateral having a line of symmetry bisecting one pair of opposite sides.
Calculation:
If two of the angles of a trapezoid are congruent, the trapezoid is isosceles. This statement is always true. Hence this statement is written as A.
Conclusion:
The given statement is always true, hence this statement is written as A.
Chapter 5 Solutions
Geometry For Enjoyment And Challenge
Additional Math Textbook Solutions
Basic Business Statistics, Student Value Edition
Elementary Statistics (13th Edition)
Calculus: Early Transcendentals (2nd Edition)
Pre-Algebra Student Edition
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Elementary Statistics: Picturing the World (7th Edition)
- In the graph below triangle I'J'K' is the image of triangle UK after a dilation. 104Y 9 CO 8 7 6 5 I 4 3 2 J -10 -9 -8 -7 -6 -5 -4 -3 -21 1 2 3 4 5 6 7 8 9 10 2 K -3 -4 K' 5 -6 What is the center of dilation? (0.0) (-5. 2) (-8. 11 (9.-3) 6- 10arrow_forwardSelect all that apply. 104 8 6 4 2 U U' -10 -8 -6 4 -2 2 4 6 10 -2 V' W' -4 -6 -8 -10 W V Select 2 correct answerts! The side lengths are equal in measure. The scale factor is 1/5. The figure has been enlarged in size. The center of dilation is (0.0) 8 10 Xarrow_forwardIn the graph below triangle I'J'K' is the image of triangle UK after a dilation. 104Y 9 CO 8 7 6 5 I 4 3 2 J -10 -9 -8 -7 -6 -5 -4 -3 -21 1 2 3 4 5 6 7 8 9 10 2 K -3 -4 K' 5 -6 What is the center of dilation? (0.0) (-5. 2) (-8. 11 (9.-3) 6- 10arrow_forward
- Qll consider the problem -abu+bou+cu=f., u=0 ondor I prove atu, ul conts. @ if Blu,v) = (b. 14, U) + ((4,0) prove that B244) = ((c- — ob)4;4) ③if c±vbo prove that acuius v. elliptic.arrow_forwardQ3: Define the linear functional J: H₁(2) R by ¡(v) = a(v, v) - L(v) Л Let u be the unique weak solution to a(u,v) = L(v) in H(2) and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u) can be rewritten under 1(u) = u Au-ub, algebraic form 1 2 Where A, b are repictively the stiffence matrix and the load vector Q4: A) Answer 1- show that the solution to -Au = f in A, u = 0 on a satisfies the stability Vullfll and show that ||V(u u)||||||2 - ||vu||2 2- Prove that Where lu-ul Chuz - !ull = a(u, u) = Vu. Vu dx + fu. uds B) Consider the bilinea forta Л a(u, v) = (Au, Av) (Vu, Vv + (Vu, v) + (u,v) Show that a(u, v) continues and V- elliptic on H(2)arrow_forward7) In the diagram below of quadrilateral ABCD, E and F are points on AB and CD respectively, BE=DF, and AE = CF. Which conclusion can be proven? A 1) ED = FB 2) AB CD 3) ZA = ZC 4) ZAED/CFB E B D 0arrow_forward
- 1) In parallelogram EFGH, diagonals EG and FH intersect at point I such that EI = 2x - 2 and EG = 3x + 11. Which of the following is the length of GH? a) 15 b) 28 c) 32 d) 56arrow_forward5) Which of the following are properties of all squares: 1. Congruent diagonals 2. Perpendicular diagonals 3. Diagonals that bisect vertex angles a) 1 and 2 only b) 1 and 3 only c) 2 and 3 only d) 1, 2, and 3arrow_forward6) In an isosceles trapezoid HIJK it is known that IJ || KH. Which of the following must also be true? a) IJ = KH b) HIJK c) HIJK d) IJ KHarrow_forward
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning