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.
