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. 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.