Congurence of Triangles: Problems with Solutions

Congurence of Triangles - SAS, SSS, ASA, SSA

Problem 1
According to the information shown in the graph, which of the following assertions are true?

I) $\measuredangle ACB\cong \measuredangle DEF$
II) $AB\cong EF$
III) $\Delta BCA\cong \Delta EFD$

Problem 2
In the following figure, $AD||BC$ and $DC||AB$. Which of the next congruences are always true?

I) $\Delta DEA\cong \Delta BEC$
II) $\Delta DEC\cong \Delta DEA$
III) $\Delta DBC\cong \Delta CAB$

Problem 3
In triangle $\Delta ABC$ from the following figure, $\measuredangle CBD=20^{o}$. $BC\cong AD$ and $CD\cong DE$, what's the angle measure $\measuredangle \alpha $ ?

Problem 4
What's the data missing so that we can state that both triangles in the following figure are congruent?

What congruence postulate is possible to use to state that $\Delta ABC\cong \Delta DEF$ ?

Problem 5
In the following figure, points $A,B,D$ are collinear(lie in the same straight line), $\Delta ABC\cong \Delta DBE,\measuredangle \alpha =36^{o}$ and $\measuredangle CBE=20^{o}$. What is the angle measure $\measuredangle DEB$ ?

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