Given: m∠A = m∠C = 90° AB ║ DC Prove: ∆ABD ≅ ∆CBD

Angle-Angle-Side (AAS)

Step-by-step explanation:

Given triangles; ΔABD and ΔCBD

  <A = <C = (right angle property)

   AB ║ DC (given)

Then,

    DA ║ CB

   <B ≅ <D (congruent property)

    DB ≅ BD (similarity property)

    <D + <B = <B + <D (complementary angles, and property of triangles)

Therefore by Angle-Angle-Side (AAS),

                 ∆ABD ≅ ∆CBD

2500

step-by-step explanation:

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4