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a.
To find:The statement “Sides HR, RM, MO and HO are congruent” is true or false.
a.
Answer to Problem 1PSA
The statement “Sides HR, RM, MO and HO are congruent” is true.
Explanation of Solution
Given information:
A rhombusHOMR with sides HR, RM, MO and HO.
Diagonals of rhombus HOMR are HM and OR which intersect at point B.
One of the two characteristics that make a rhombus unique is that its four sides are equal in length, or congruent. The other identifying property is that opposite sides are parallel.
b.
To find: The statement “Diagonals HM and RO are perpendicular” is true or false.
b.
Answer to Problem 1PSA
The statement “Diagonals HM and RO are perpendicular” is true.
Explanation of Solution
Given information:
A rhombus HOMR with sides HR, RM, MO and HO.
Diagonals of rhombus HOMR are HM and OR which intersect at point B.
A wonderful and rare property of a rhombus is that its diagonals are always perpendicular to each other. You can see this for yourself if you lay down your four straight objects to make a rhombus and then draw in diagonals. No matter what
c.
To find: The statement “Diagonals HM and RO bisects the angles” is true or false.
c.
Answer to Problem 1PSA
The statement “Diagonals HM and RO bisects the angles” is true.
Explanation of Solution
Given information:
A rhombus HOMR with sides HR, RM, MO and HO.
Diagonals of rhombus HOMR are HM and OR which intersect at point B.
A diagonal of a rhombus splits a triangle into two congruent
Thus, diagonal HM bisects vertex angles at H and M. Diagonal RO bisects vertex angles at R and O.
d.
To find: The statement “Diagonals HM and RO bisects each other” is true or false.
d.
Answer to Problem 1PSA
The statement “Diagonals HM and RO bisects each other” is true.
Explanation of Solution
Given information:
A rhombus HOMR with sides HR, RM, MO and HO.
Diagonals of rhombus HOMR are HM and OR which intersect at point B.
The diagonal of a rhombus bisect each other at right angles. In any rhombus, the diagonals bisect each other at right angles, i.e. each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.
Diagonals HM and RO bisect each other at point Q.
e.
To find: The statement “Diagonals HM and RO are congruent” is true or false.
e.
Answer to Problem 1PSA
The statement “Diagonals HM and RO are congruent” is false.
Explanation of Solution
Given information:
A rhombus HOMR with sides HR, RM, MO and HO.
Diagonals of rhombus HOMR are HM and OR which intersect at point B.
If you look in the diagram, the diagonals are not equal, but the sides are equal. One thing you may notice, though, is that the diagonals are perpendicular to each other and they bisect each other.
So, the diagonals are sometimes congruent, but they are always perpendicular bisectors.
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