Question

problem 24
clear
statements
reasons
exit
given: $\delta bcf \cong \delta bhg$,
$fe = ge$
prove: $\delta bce \cong \delta bhe$

1. $\delta bcf \cong \delta bhg$
2. given
3. click here to insert
4. corresponding parts of congruent triangles are congruent (c.p.c.t.c.)
5. $fe = ge$
6. given
7. click here to insert
8. click here to insert
9. $ce = cf + fe$ and

5.

Explanation:

Step1: Extract congruent segments

From $\Delta BCF \cong \Delta BHG$, by C.P.C.T.C., we get $CF = HG$ and $BF = BH$.

Step2: Add equal segments to congruent ones

Given $FE = GE$, add to congruent segments:
$CF + FE = HG + GE$, so $CE = HE$.

Step3: Identify shared side

Side $BE$ is common to both $\Delta BCE$ and $\Delta BHE$, so $BE = BE$.

Step4: Apply SSS congruence

We have $BC = BH$ (from C.P.C.T.C.), $CE = HE$, $BE = BE$. By SSS congruence, $\Delta BCE \cong \Delta BHE$.

Answer:

Completed Statements and Reasons:

1. $\Delta BCF \cong \Delta BHG$ | 1. Given
2. $BC = BH$, $CF = HG$ | 2. Corresponding Parts of Congruent Triangles are Congruent (C.P.C.T.C.)
3. $FE = GE$ | 3. Given
4. $CE = HE$ | 4. Addition Property of Equality ($CF+FE=HG+GE$)
5. $BE = BE$ | 5. Reflexive Property of Congruence
6. $\Delta BCE \cong \Delta BHE$ | 6. Side-Side-Side (SSS) Congruence Postulate