3: Bob has four boards of equal length and wants to be sure that his garden is square. How can he ensure the garden is square by
only measuring length? A: Arrange the boards so diagonals bisect each other
B: Arrange the boards so that the diagonals are congruent
C: Arrange the boards so that the diagonals are perpendicular
D: Not possible without the ability to measure a right angle
4: Find the measures of the base angles in the isosceles trapezoid shown below.
19x+8 11x+16
A: 49°
B: 46°
C: 38°
D: 27°
7: In the rhombus, m∠1=10x, m∠2=x + y, and m∠3= 5z. Find the values of x, y, and z.
10: Find the values of x and y in the kite shown below.
https://lh6.googleusercontent.com/j5Sk38PdH1gbdH4TFJ2eRGP6qzA0Ym7L3Zgeu6BqgbrcU6YIuBXTt1ThxxdzrBaMEJLr8gK6vg=w413
11: Complete the missing reasons in the proof below.
3. I believe the answer is C & A, arrange the boards so that the diagonals bisects and are perpendicular. A rhombus is a Quadrilateral with all its sides equal to each other. The diagonals of a rhombus are perpendicular to each other and bisects each other.
4.The corresponding pairs of base angles of a trapezoid add up to 180 degrees, (they are supplementary), While all the angles (the four angles add up to 360 degrees) Therefore; in this case the two angles are equal hence, 19x + 8 = 11x+16 solving for x x = 1 substituting x in either of the expression The angle = 27 °
5. The diagonals of a rhombus bisects each other at right angles; the are perpendicular, hence, m∠1= 10x = 90 x = 9
m∠2 = x + y =90 but x = 9, thus, y = 81
m∠3 = 5z= 90 z =18
10. A kite is a Quadrilateral with two equal sides and the other two sides equal. thus, y-4 = 5x+2 and x +22 = 3x +10 solving for x x+22 = 3x +10 2x = 12 x = 6 y-4 = 5x +2 y-4 = 5(6) +2 y = 36.
11.a. RHOM is a Quadrilateral with four equal sides b. The four sides RH, OH, OM, and RM are equal, They are all congruent c HM and HM is the diagonal, which forms the corresponding sides of triangle MRH and triangle MOH d. Triangle MRH and triangle MOH are congruent, SSS, and similar to each other.
Step-by-step explanation: Multiply -36 and 163/9 to get -652. Add 652 to both sides then add 130 and 652 to get 782. Divide both sides by -12 then reduce the fraction 782/-12 to lowest terms by extracting and canceling out 2. The system is now solved.
