Question

given: be=ce, ed=ea
prove: bd=ca
statements reasons
be = ce,ed = ea given
be + ed = ce + ed addition property
be + ed = ce + ea substitution
be + ed = bd, ce + ea = ca ???
bd = ca substitution
fill in the missing reason.
segment addition postulate
definition of vertical angles
definition of congruent
angle addition postulate

Explanation:

The Segment Addition Postulate states that if we have three collinear points, say \(X\), \(Y\), and \(Z\), then \(XY + YZ=XZ\). In the context of line - segments in the problem, since \(B\), \(E\), and \(D\) are collinear and \(C\), \(E\), and \(A\) are collinear, we can say that \(BE + ED = BD\) and \(CE+EA = CA\) based on this postulate.

Answer:

Segment Addition Postulate