The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.
<h3>What is a Rhombus?</h3>
A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.
<h3>What is the above proof?</h3>
- ∠DEC ≅ ∠BFC Reason = All Right Angles with Equal dimensions are congruent.
- ∠C ≅ ∠C Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.
- Δ DEC ≅ Δ BFC Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
- ≅ Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.
- ABCD is a Rhombus Reason = Its sides are all congruent.
Learn more about Rhombus at;
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1/5 + 1/3·x > 1/2·x - 1/4
1/3·x - 1/2·x > - 1/4 - 1/5
2/6·x - 3/6·x > - 5/20 - 4/20
- 1/6·x > - 9/20
1/6·x < 9/20
x < 54/20
x < 27/10
x < 2.7
15 15 15 15 15 15 15 15 15 15
If you know the center is at (-1,3), then find r by writing out the standard formula for the equation of a circle, as follows:
(x-2)^2 + (y-5)^2 = r^2
We still have the other point to deal with: (-4,1). Subst. -4 for x in this equation, and 1 for y:
(-4-2)^2 + (1-5)^2 = r^2. Then 36 + 16 = r^2,
and 52 = r^2, so that the radius is positive sqrt(52).
You could write that as sqrt(4)sqrt(13) = 2sqrt(13). Take your pick.