Point M is the midpoint of segment AB. If AM = 50 – 3x and MB = –20 + 4x, find the value of x. x = -10 x = 10 x = -20 x = 20
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Answer:
<em>DF = 10 units</em>
<em>EG = 5.04</em>
Step-by-step explanation:
<u>Properties of Rhombus es</u>
- All Sides Of The Rhombus Are Equal.
- The Opposite Sides Of A Rhombus Are Parallel.
- Opposite Angles Of A Rhombus Are Equal.
- In A Rhombus, Diagonals Bisect Each Other At Right Angles.
- Diagonals Bisect The Angles Of A Rhombus.
The image contains a rhombus with the following data (assume the center as point O):
DO = 5 units
GF = 5.6 units
4. Calculate DF
Applying property 4, diagonals bisect each other, thus the length of DF is double the length of DO, i.e. DF=2*5 = 10:
DF = 10 units
5. Calculate
Applying property 4 in triangle EFO, the center angle is 90°, thus angle EFO has a measure of 90°-62°=28°.
Applying property 5, this angle is half of the measure of angle EFG and angle DFG has the same measure of 28°.
6. FG is the hypotenuse of triangle OFG, thus:
EG is double OG: OG=2*2.52=5.04
EG = 5.04