Triangle a″b″c″ is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. which equation shows the correct relationship between δabc and δa″b″c″?
coordinate plane with triangle abc at a negative 3 comma 3, b 1 comma negative 3, and c negative 3 comma negative 3
segment ab over segment a double prime b double prime = the square root of 13 over 2 times the square root of 13
segment c double prime a double prime over segment ca = the square root of 16 over 2 times the square root of 16
segment ab = zero point two segment a double prime b double prime
segment c double prime a double prime = zero point two segment ca

segment AB over segment A double prime B double prime = the square root of 13 over 2 times the square root of 13

Step-by-step explanation:

Triangle ABC has vertices at points A(-3,3), B(1,-3) and C(-3,-3).

1. Reflection over x = 1 maps vertices A, B and C as follows

2. Dilation by a scale factor of 2 from the origin has the rule

(x,y)→(2x,2y)

So,

See attached diagram for details

Note that

so

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