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Elodia [21]
3 years ago
7

Jim has made a dartboard using two concentric circles, one blue and one yellow. The distance from the center to the edge of the

blue circle is 8 inches, while from the center to the edge of the yellow circle it is 11 inches. Jim plans to play a game with his friend Randolph, in which the blue region is Jim's and the yellow region is Randolph's.
Is the game FAIR?
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
8 0

Answer:

No; the blue region is larger.

Step-by-step explanation:

The area of the blue region is 64π = 200.96 square inches, while the area of the yellow region is 121π - 64π = 178.98 square inches.

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Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why DEF=JK
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A) AAS; B) LA; C) ASA

Step-by-step explanation:

AAS is the Angle-Angle-Side congruence statement.  It says that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of a second triangle, then the triangles are congruent.  In these triangles, ∠E≅∠K, ∠F≅∠L, and DE≅JK.  These are two angles and a non-included side; this is AAS.

LA is the leg-acute theorem.  It states that if a leg and acute angle of one triangle is congruent to the corresponding leg and acute angle of another triangle, then the triangles are congruent.

The leg we have congruent from each triangle is DE and JK.  We also have ∠E≅∠K and ∠F≅∠L, both pairs of which are acute.  This is the LA theorem.

ASA is the Angle-Side-Angle congruence statement.  It says that if two angles and an included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the triangles are congruent.  

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3 years ago
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</span><span><em>Don't forget to rate this answer the Brainliest!</em>

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