Question

in the figure p is the incenter of isosceles rst what type of triangle is rpt? Thank you in advance .

Answer 1

Answer:

$\Delta \text{RPT is an isosceles triangle}$

Step-by-step explanation:

As in the triangle RST,

$RS=ST\ \ \ \Rightarrow m\angle SRT=m\angle STR$

Because if in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another.

Incenter is obtained by the Intersection of a triangle's three angle bisectors and it is equidistant from the three sides of the triangle.

So, RP and TP are the angle bisectors of ∠R and ∠T respectively.

$\Rightarrow \dfrac{m\angle SRT}{2}=\dfrac{m\angle STR}{2}$

$\Rightarrow m\angle PRT=m\angle PTR$

$\Rightarrow PR=PT$

$\Rightarrow \Delta \text{RPT is an isosceles triangle}$

Answer 2

Isosceles triangles mean that 2 sides of the triangle are congruent. Since triangle RST is isosceles and P is its incenter, that means that PT and PR must be congruent, also. PRT is an isosceles triangle.