Question 11
1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)
2) [tex]\angle A \cong \angle A[/tex] (reflexive property)
3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)
4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)
Question 12
1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)
2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)
3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)
4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)
5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)
6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)
7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)
Note: I changed the names of the segments in Question 11 because of the word filter.
