9514 1404 393
Answer:
a. 12 cm
b. 90°
c. 60°
Step-by-step explanation:
The relevant relationships are ...
- all sides of a rhombus have the same length
- the diagonals of a rhombus are perpendicular bisectors of each other
- the diagonals of a rhombus divide the figure into 4 congruent triangles
__
a) The perimeter, 48 cm, is the sum of four equal side lengths, so any given side is (48 cm)/4 = 12 cm.
GH = 12 cm
__
b) Angle EJF is where the diagonals meet. It is a right angle.
∠EJF = 90°
__
c) Angle EFJ is the complement of the one marked, so is 30°. Angles EHJ and GHJ are congruent to that, so both are 30°. Angle EHG is the sum of those two congruent 30° angles, so is ...
∠EHG = 60°
