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.
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