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2 years ago

7

I need to know what this is ASA SSS SAS AAS?

1 answer:

Dafna1 [17]2 years ago

4 0

All of those are congruency short-cuts. S stands for side, A stands for Angle. Using these shortcuts, we can prove congruency in triangles easier. in the problem above, we are given a pair of angles that are congruent and a side that is congruent. Using the vertical angle theorem, we have two angles and 1 side so both those triangles would be congruent by AAS.

There are two congruency methods that don't work. There's SSA and AAA, For number 3, it would be congruent by ASA, not AAS, and for number 4, it would be congruent by AAS, or SAA, SAA is more used.

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Required

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$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

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$0.626 = P(A) + P(B) - 0.144$

Collect like terms

$P(A) + P(B) = 0.626 + 0.144$

$P(A) + P(B) = 0.770$

Make P(A) the subject

$P(A) = 0.770 - P(B)$

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$0.144 = P(A) * P(B)$

$P(A) * P(B) = 0.144$

Substitute: $P(A) = 0.770 - P(B)$

$[0.770 - P(B)] * P(B) = 0.144$

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Represent P(B) with x

$0.770x - x^2 = 0.144$

Rewrite as:

$x^2 - 0.770x + 0.144 = 0$

Expand

$x^2 - 0.45x - 0.32x + 0.144 = 0$

Factorize:

$x[x - 0.45] - 0.32[x - 0.45]= 0$

Factor out x - 0.45

$[x - 0.32][x - 0.45]= 0$

Split

$x - 0.32= 0 \ or\ x - 0.45= 0$

Solve for x

$x = 0.32\ or\ x = 0.45$

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So, we have:

$P(B) = 0.32 \ or \ P(B) = 0.45$

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So, we have:

$P(A) = 0.770 - 0.32 \ or\ P(A) =0.770 - 0.45$

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Since:

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Then:

$P(A) = 0.45$

$P(B) = 0.32$

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