Part a.
Based on these two facts
- Angle ABC = angle DEC (due to the same angle arc markings)
- Angle ACB = angle DCE (since vertical angles are congruent)
This means the triangles are similar through the AA (angle angle) similarity postulate.
One similarity statement would be [tex]\triangle ABC \sim \triangle DEC[/tex]
The order of the letters of D,E,C is based on A,B,C so that the corresponding congruent angles pair up. A pairs with D, B pairs with E, C pairs with itself.
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Part b.
Similar to part a. These two triangles are similar because
- Angle VXW = Angle ZXY (vertical angles)
- Angle WVX = Angle YZX (alternate interior angles)
So again we are using the AA similarity postulate.
The alternate interior angles are only congruent because of the parallel lines WV and YZ
One similarity statement would be [tex]\triangle VWX \sim \triangle ZYX[/tex]
Again, order matters.
