Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
<h3>What is the Pythagoras Theorem?</h3>
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In △ABD and △ACB,
∠A = ∠A (common)
∠ADB = ∠ABC (both are right angles)
Thus, △ABD ∼ △ACB (by AA similarity criterion)
Similarly, we can prove △BCD ∼ △ACB.
Thus △ABD ∼ △ACB,
Therefore, AD/AB = AB/AC.
We can say that AD × AC = AB².
Similarly, △BCD ∼ △ACB.
Therefore,
CD/BC = BC/AC.
We can also say that
CD × AC = BC².
Adding these 2 equations, we get
AB² + BC² = (AD × AC) + (CD × AC)
AB² + BC² =AC(AD +DC)
AB² + BC² = AC²
Hence proved
Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
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Answer:

Step-by-step explanation:
Before number line can be drawn, there is need to find the value of x in the inequality given. Thus,

Divide both sides by 2


The number line is indicated in the attached picture.
we have been asked to find the sum of the series

As we know that a geometric series has a constant ratio "r" and it is defined as

The first term of the series is 
Geometric series sum formula is

Plugin the values we get

On simplification we get

Hence the sum of the given series is
Answer: 5 is the GCF
Step-by-step explanation: It just is