Therefore, An equiangular triangle can never be scalene. Finding Measures in a Triangle Find the measures of ∠P, ∠Q, and ∠R. The largest side will be opposite the #90^o#. On the other hand a scalene triangle has unequal sides. From the corollary above, this triangle is also equiangular. As another example, the sides opposite the base angles of an isosceles triangle have sides that are equal because the base angles are equal. So, by the Corollary to the Base Angles Theorem, PQR is equiangular. In this lesson you will prove that an isosceles triangle also has two congruent angles opposite the two congruent sides. 4.7 Use Isosceles and Equilateral Triangles 265 EXAMPLE 2 Find measures in a triangle Find the measures of ∠ P,∠ Q, and ∠ R. The diagram shows that nPQR is equilateral. SOLUTION a.Notice that xrepresents the measure of an angle of an equilateral triangle.

3x° = 180° Apply the Triangle Sum Theorem. Since, in case of equiangular triangle all the sides are equal. Finally, the side opposite the #60^o# will fall somewhere in between.

On the other hand a scalene triangle has unequal sides. Therefore, by the Corollary to the Base Angles Theorem, nPQR is equiangular. Using Equilateral and Isosceles Triangles a.Find the value of x. b.Find the value of y. Find algebraic equation for angles in isosceles triangle [8] 2020/02/26 06:10 Male / 20 years old level / High-school/ University/ Grad student / Very / Purpose of use Improve your math knowledge with free questions in "Scalene, isosceles, and equilateral triangles" and thousands of other math skills. corollaries below state that a triangle is equilateral if and only if it is equiangular. SOLUTION The diagram shows that PQR is equilateral. 39, p. 258 READING The corollaries state that a triangle is equilateral if and only if it is equiangular. A 30-60-90 triangle will have its smallest side opposite the #30^o#. If a triangle is equiangular, then it is equilateral. Proof Ex. The congruent sides of the isosceles triangle are called the legs of the triangle. An isosceles triangle is defined as a triangle that has at least two congruent sides. So, m∠P = m∠Q = m∠R.