Question 1099765: Can you please help me answer a proof question? B is the midpoint of segment AE; B is the midpoint of segment CD. Prove: angle ADB is congruent to angle ECB. (Triangles, they are triangles)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! AB is congruent with EB because B is the midpoint of AE
BC is congruent with BD because B is the midpoint of CD
Point B, belonging to lines AE and CD is the intersection of those lines
Two pairs of vertical angles are formed by the intersection of those lines.
Angles ABD and EBC are one of those vertical pairs.
Because they are a pair of vertical angles, angles ABD and EBC are congruent.
Triangles ABD and EBC are congruent by side-angle-side congruency,
because they have
AB congruent with EB,
BD congruent with BC,
and between those pairs of congruent sides they have
angle ABD congruent with angle EBC.
Because Corresponding Parts of Congruent Triangles are Congruent (CPCTC),
angle ADB is congruent with angle ECB.
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