Math  /  Geometry

QuestionGiven: DED E bisects BEC\angle B E C and BECE\overline{B E} \cong C E. Prove: ADBADC\triangle A D B \cong \triangle A D C. Step DE\overline{D E} bisects BEC\angle B E C BECE\overline{B E} \cong \overline{C E}
Given try Type of Statement

Studdy Solution
Apply the Side-Angle-Side (SAS) Congruence Postulate:
- BECE \overline{BE} \cong \overline{CE} (Given) - BEDCED \angle BED \cong \angle CED (Angle Bisector) - AD \overline{AD} is common to both ADB \triangle ADB and ADC \triangle ADC .
By the SAS Congruence Postulate, we have:
ADBADC \triangle ADB \cong \triangle ADC
The triangles ADB \triangle ADB and ADC \triangle ADC are congruent.

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