Given: sv is parallel to tu and triangle svx is congruent to triangle utxprove: vuts is a parallelogram

Hence it is proved that VUTS is a parallelogram.

Step-by-step explanation:

Since ΔSVX ≅ΔUTX AND SV║TU

In the similar triangles ΔSVX and ΔUTX⇒ ∠TVS =∠UTV and ∠VSU =∠SUT

as they are alternate angles therefore ∠VXS=∠UXT. Since all angles of these triangles are same then sides of these triangles will be of same length.Therefore SV=TU.

Similarly in triangles ΔUXV and ΔSXT

∠VSU=∠SUT (alternate angles) then ∠UST=∠SUV (remaining angles of ∠VST and ∠TUV).

And ∠SVT = ∠UTV then ∠TVU=∠VTS (remaining angles of ∠SVU and ∠UTS)

Since these angles are alternate angles therefore VU║ST.

And we know all angles of ΔUVX are equal to angles of ΔSXT

Therefore sides of these triangles will be equal VU= ST.

Now we can say that sides ST and VU are parallel and equal.

Since all opposite sides of VSTU are equal and parallel to each other therefore VSTU is a parallelogram.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c

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