Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse?
2 answers:
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Prove:
Using mathemetical induction:
P(n) =
for n=1
P(n) = = 6
It is divisible by 2 and 3
Now, for n=k,
P(k) =
Assuming P(k) is divisible by 2 and 3:
Now, for n=k+1:
P(k+1) =
P(k+1) =
P(k+1) =
Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also
divisible by 2 and 3.
Hence, by mathematical induction, P(n) = is divisible by 2 and 3 for all positive integer n.
The coordinates of the endpoints of the mid-segment of Δ XYZ that parallel to XZ are (1 , 6) and (1 , 3)
Step-by-step explanation:
In a triangle the segment which joining the mid points of two sides:
- Parallel to the 3rd side
- Its length is equal half the length of the 3rd side
- It's called the mid-segment of the triangle
In Δ XYZ
∵ Vertex X is (0 , 7)
∵ Vertex Y is (2 , 5)
∵ Vertex Z is (0 , 1)
∵ The mid-segment of Δ XYZ is parallel to XZ
- The mid-segment intersects the other two sides of the Δ
at their mid-points
∴ The mid-segment intersects XY and YZ at their midpoints
∴ The endpoints of the mid-segment are the midpoints of
XY and YZ
The mid point of a segments whose endpoints are and
is
∵ X = (0 , 7) and Y = (2 , 5)
∴ = 0 and
= 2
∴ = 7 and
= 5
∵ The mid point of XY =
∴ The mid point of XY =
∴ The mid point of XY = (1 , 6)
∵ Z = (0 , 1) and Y = (2 , 5)
∴ = 0 and
= 2
∴ = 1 and
= 5
∵ The mid point of ZY =
∴ The mid point of ZY =
∴ The mid point of ZY = (1 , 3)
∵ The endpoints of the mid-segment are the midpoints of
XY and YZ
∴ The end points of the mid segments are (1 , 6) and (1 , 3)
The coordinates of the endpoints of the mid-segment of Δ XYZ that parallel to XZ are (1 , 6) and (1 , 3)
Learn more:
You can learn more about the mid-point in brainly.com/question/5223123
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