Use the drawing provided to explain the following theorem.“The three angle bisectors of the angles of a triangle are concurrent.”Given: 
, 
, and 
are the angle bisectors of the angles of 
Prove: , , and are concurrent at point Z
What will be an ideal response?
and 
. Because bisects 
, every point on 
(including Z) is equidistant from the sides of .With 
and 
, it follows that 
. With respect to 
, also note
that 
. Because Z lies on angle bisector 
, we also have 
. By the Transitive Property of Congruence, 
. With point Z being equidistant from the sides of 
, Z must also lie on angle bisector 
. Thus, , , and are concurrent at point Z.
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Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators.y2 = 150
A. {5
}
B. {±6
}
C. {6
}
D. {±5
}
Rewrite as a single logarithm.2 log2(2x + 5) + 6 log2(6x + 1)
A. 12 log2(2x + 5)(6x + 1)
B. log2((2x + 5)2 + (6x + 1)6)
C. log2(2x + 5)2(6x + 1)6
D. log2
Solve the problem. Round to the nearest tenth.The roof of a building is in the shape of the hyperbola y2 - 3x2 = 39, where x and y are in meters. Refer to the figure and determine the height, h, of the outside walls.
a = b = 7 m
A. 186 m B. 13.6 m C. 52 m D. 7.2 m
Solve the triangle.a = 60, b = 8, C = 105°
A. c = 65.45, A = 69.9°, B = 5.1° B. c = 68.35, A = 65.9°, B = 9.1° C. c = 62.55, A = 67.9°, B = 7.1° D. no triangle