Math  /  Geometry

QuestionFill in the missing statement and reason of the proof below. Given: FDFC\overline{F D} \cong \overline{F C} and FDEFCE\angle F D E \cong \angle F C E. Prove: ADBBCA\triangle A D B \cong \triangle B C A. p Statement FDFC\overline{F D} \cong \overline{F C} FDEFCE\angle F D E \cong \angle F C E FF\angle F \cong \angle F ACFBDF\triangle A C F \cong \triangle B D F
Reason
Given
Reflexive Property ASA
Type of Statement DABCBAABAB\begin{aligned} \angle D A B & \cong \angle C B A \\ \overline{A B} & \cong \overline{A B} \end{aligned} ADBCADBBCA\begin{array}{c} \overline{A D} \cong \overline{B C} \\ \triangle A D B \cong \triangle B C A \end{array}
In a triangle, angles opposite of congruent sides are congruent
Reflexive Property Congruent segments subtracted from congruent segments form congruent segments
SAS

Studdy Solution
Complete the proof using congruence postulates:
1. Given: FDFC\overline{F D} \cong \overline{F C}
2. Given: FDEFCE\angle F D E \cong \angle F C E
3. FF\angle F \cong \angle F by the Reflexive Property
4. ACFBDF\triangle A C F \cong \triangle B D F by ASA (Angle-Side-Angle)
5. DABCBA\angle D A B \cong \angle C B A because in a triangle, angles opposite of congruent sides are congruent
6. ABAB\overline{A B} \cong \overline{A B} by the Reflexive Property
7. ADBC\overline{A D} \cong \overline{B C} because congruent segments subtracted from congruent segments form congruent segments
8. ADBBCA\triangle A D B \cong \triangle B C A by SAS (Side-Angle-Side)

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