Question

use the diagram.
select all the true statements.
a. ( bc>fg )
b. ( fg = 10 )
c. ( eg = 12 )
d. ( mangle ced=mangle cab )
e ( mangle cab>mangle ced )

Explanation:

Step1: Analyze triangle congruence

By SSS (Side - Side - Side) congruence, \(\triangle ABC\cong\triangle DEF\). So \(BC = EF\), \(AC=DE\), \(AB = DF\). Also, \(\angle CAB=\angle CED\) (corresponding angles of congruent triangles).

Step2: Check each option

• Option A: Since \(BC = EF\) and there is no information to suggest \(EF>FG\), \(BC>FG\) is not necessarily true.
• Option B: Because \(\triangle ABC\cong\triangle DEF\), \(AB = DF = 10\). And by SSS for \(\triangle DEF\) and \(\triangle FEG\) (assuming appropriate side - side relations from the diagram markings), \(FG=DF = 10\).
• Option C: From the congruence and side - length relations in the diagram (assuming proper segment equalities from markings), \(EG = 12\).
• Option D: As \(\triangle ABC\cong\triangle DEF\) (by SSS), \(\angle CAB=\angle CED\) (corresponding angles), so \(m\angle CED=m\angle CAB\).
• Option E: Since \(m\angle CED=m\angle CAB\), \(m\angle CAB>m\angle CED\) is false.

Answer:

B. \(FG = 10\), C. \(EG = 12\), D. \(m\angle CED=m\angle CAB\)