Again, since ∠ DCE and ∠ ACB are vertical angles we know they are congruent, which means m∠ ACB=110^(∘) as well.
To find the base angles of △ ABC we remember that this is also an isosceles triangle, so by the Base Angles Theorem ∠ A and ∠ B are congruent.
m∠ A+m∠ B+ 110^(∘) = 180^(∘)
Let's substitute one of the base angle measures with the other and solve the equation.
The base angles of △ ABC are also 35^(∘) each. Therefore, we know that the two triangles have three pairs of congruent corresponding angles, which means they are similar triangles.
b The following flowchart assumes that we know the angles of both triangles.
c When writing a statement claiming that two shapes are similar, you have to make sure that the letters of corresponding vertices come in the same order. Cheri's statement tells us that A and D are corresponding vertices and B and E are corresponding vertices.
In Roberta's statement, A and E are corresponding vertices and B and D are corresponding vertices.
Both Cheri and Roberta can be correct, as we are dealing with similar isosceles triangles. This means the base angles are all congruent, so it does not matter which of them you pair up.
