Question

#3: Explain if the triangles are similar using AA-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)

Answer 1

AS shown in the figure :

There are two right triangles

For the triangle SYE :

m∠ Y = 90

m∠ E = 39

So, m∠S = 180 - ( 90 + 39 ) = 51

For the triangle WCH :

m∠ C = 90

m∠ W = 51

m∠ H = 180 - ( 90 + 51 ) = 39

So, the triangles SYE and WCH have the following :

m∠ Y = m∠ C = 90

m∠ E = m∠ H = 39

m∠ S = m∠ W = 51

So, the triangles are similar by AAA [ angle - angle - angle Postulate ]