The circle is inscribed in triangle prt.

which statements about the figure are true? check all that apply.

- the perimeter of the triangle is 19 units.
- tu ≊ ts
- pu ≅ tu
- the length of line segment pr is 13 units.
- the length of line segment tr is 10 units.

We are given,

a circle inscribed in a triangle prt.

based on the figure given where pu = 8, ut = 6; sr = 5

we can conclude from the figure that the following statements are:

the perimeter of the triangle is 19 units. false. since there are already given values of 8+6+5 = 19 which are just part of the triangle. therefore the perimeter should be more than 19. 

tu ≊ ts true

pu ≅ tu false

pu = 8 and tu = 6; obviously, they are not equal, thus, not congruent.

the length of line segment pr is 13 units. false
pr should be equal to pt and pt is equal to 14. 

the length of line segment tr is 10 units. true

we know that

if the circle is inscribed in triangle prt

then

tu ≊ ts

pu ≊ pq

rp ≊ rs

statements

case a) the perimeter of the triangle is units

the statement is false

we know that

perimeter of the triangle is equal to

case b) tu ≊ ts

the statement is true

we know that

so

tu ≊ ts

case c) pu ≅ tu

the statement is false

we know that

so

case d) the length of line segment pr is units

the statement is true

we know that

case e) the length of line segment tr is units

the statement is false

we know that

therefore

the answer is

tu ≊ ts

the length of line segment pr is units

8 neighbors will get half of a pie