In triangle STU, we have ST = SU = 22 and TU = 8. Let M be the midpoint of and N be on such that is an altitude of triangle STU. If and intersect at X, then what is SX?

4√13  

Step-by-step explanation:

1. Calculate the length of SN

Your triangle (below) is a relatively tall isosceles triangle.

∆STN is a right triangle, so we can use Pythagoras theorem to calculate the length of SN.

SN² + NT² = ST²

SN² + 4² =22²

SN² + 16 = 484

SN² = 468

SN = √468 = 6√13

2. Calculate the length of SX

UM and SN are lines from an angle to the centre of the opposite side, so they are medians.

The medians of a triangle meet at a single point, X — the centroid.

Another characteristic is that the centroid divides each median into segments in a 2:1 ratio.

Thus,

SX = ⅔SN = ⅔ × 6√13 = 4√13

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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