Prove that an equila'teral triangle is equian gular.
Answers
Answer:we use the said theorem to prove that equilateral triangles are equiangular.
equilateral triangle
Theorem
Equilateral triangles are equilangular.
Given
Equilateral triangle PQR
What To Show
\angle P \cong \angle Q \cong \angle R.
Proof
\overline{PQ} \cong \overline{PR} since all sides of an equilateral triangle are congruent.
\angle Q \cong \angle R the angles opposite to the two congruent sides of a triangle are congruent (Isosceles Triangle Theorem)
\overline{PQ} \cong \overline{QR} since all sides of an equilateral triangle are congruent.
\angle R \cong \angle P, again, by the Isosceles Triangle Theorem
Now, since \angle Q \cong \angle R and \angle R \cong \angle P, by the Transitivity Property of Equality, \angle Q \cong \angle P.
Therefore, \angle P \cong \angle Q \cong \angle R.
So, equilateral triangles are equiangular.
Step-by-step explanation: