Question

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.

https://lh5.googleusercontent.com/cWLeD4MjTIcE_FCOeGholJBhW7kmjTbKtsL1o3fmsRMMUlfgHhy2fSjXSWFab2Qg5enzQgO41A=w720

Answer 1

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.