Gideon has prepared the following two-column proof below. he is given that ∠oln ≅ ∠lno and he is trying to prove that δole ≅ δone.

triangle oln, where angle oln is congruent to angle lno

step statement reason
1 ∠oln ≅ ∠lno given
2 draw oe as a perpendicular bisector to ln by construction
3 m∠leo = 90° definition of a perpendicular bisector
4 m∠neo = 90° definition of a perpendicular bisector
5 le ≅ en definition of a perpendicular bisector
6 ol ≅ on cpctc
7 ∠leo ≅ ∠neo substitution property of equality
8 δole ≅ δone angle-side-angle (asa) postulate

gideon made two errors in the proof. identify and correct the errors.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

found it xd it ok yt

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc