To prove that triangles TRS and SUT are congruent we can follow these statements:
1.- SR is perpendicular to RT: Given
2.-TU is perpendicular to US: Given
3.-Angle STR is congruent with angle TSU: Given.
4.-Reflexive property over ST: ST is congruent with itself (ST = ST)
From here, we can see that both triangles TRS and SUT have one angle of 90 degrees, another angle that they both have, and also they share one side (ST) ,then:
5.- By the ASA postulate (angle side angle), triangles TRS and SUT are congruent
If it is a triangle h is height and b is base.
Answer:
The center of the circle is
.
Step-by-step explanation:
The center of the circle is the midpoint of the segment between the endpoints. We can determine the location of the center by this vectorial expression:
(1)
Where:
- Center.
,
- Location of the endpoints.
If we know that
and
, then the location of the center of the circle is:



The center of the circle is
.
Answer:

Step-by-step explanation:
We have the expression:

The first thing we want to do, is to have the same denominator in both equations, then we need to multiply the first term by (2/2), so the denominator becomes 4*x
We will get:

Now we can directly add the terms to get:

We can't simplify this anymore