Question

attempts 0 allowed attempts 1
select all the true statements about the figure below.

□△adb≅△aeb
□bd≅be
□∠bdc≅∠bec
□ab≅be
□△cdb≅△cae
□∠abd≅∠abe

Explanation:

Step1: Check for congruent triangles using SSS (Side - Side - Side)

In \(\triangle ADB\) and \(\triangle AEB\), \(AD = AE\) (given), \(AB=AB\) (common side), \(BD = BE\) (from \(\triangle CDB\cong\triangle CEB\) by SSS as \(CD = CE\), \(CB = CB\), \(DB = EB\)). So, \(\triangle ADB\cong\triangle AEB\) (by SSS).

Step2: Check for congruent angles

Since \(\triangle ADB\cong\triangle AEB\), \(\angle ABD\cong\angle ABE\) (corresponding parts of congruent triangles).

Step3: Check other statements

• \(BD\cong BE\): True as \(\triangle CDB\cong\triangle CEB\) (SSS: \(CD = CE\), \(CB = CB\), \(DB = EB\)).
• \(\angle BDC\cong\angle BEC\): False. There is no information or congruence relation to support this.
• \(AB\cong BE\): False. No indication from given markings.
• \(\triangle CDB\cong\triangle CAE\): False. \(CD = CE\), but other sides (\(CB

eq CA\), \(DB
eq AE\)) do not match for SSS congruence.

Answer:

\(\triangle ADB\cong\triangle AEB\), \(BD\cong BE\), \(\angle ABD\cong\angle ABE\)