If the triangles are similar, find the scale factor from triangle DEF to triangle ABC.
2 answers:
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9514 1404 393
Answer:
- ∠QSR = 78°
- ∠SQR = 51°
Step-by-step explanation:
The measure of an inscribed angle (QTR) is half the measure of the arc it intercepts. The measure of an arc is the same as the measure of the central angle it intercepts. So, we have ...
∠QSR = 2×∠QTR
∠QSR = 2×39°
∠QSR = 78°
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Sides SQ and SR are radii of circle S, so are the same length. That means triangle QRS is an isosceles triangle and the base angles SQR and SRQ are congruent. The sum of angles in a triangle is 180°, so we have ...
∠QSR + 2(∠SQR) = 180°
78° + 2(∠SQR) = 180° . . . . fill in the value we know
2(∠SQR) = 102° . . . . . . . . . subtract 78°
∠SQR = 51° . . . . . . . . . . . . .divide by 2
You can find counterexamples to disprove this claim. We have positive integers that are perfect square numbers; when we take the square root of those numbers, we get an integer.
For example, the square root of 1 is 1, which is an integer. So if y = 1, then the denominator becomes an integer and thus we get a quotient of two integers (since x is also defined to be an integer), the definition of a rational number.
Example: x = 2, y = 1 ends up with which is rational. This goes against the claim that
is always irrational for positive integers x and y.
Any integer y that is a perfect square will work to disprove this claim, e.g. y = 1, y = 4, y= 9, y = 16. So it is not always irrational.