Question

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suppose ( \triangle fmn cong \triangle hqr )
which congruency statements are true?
select each correct answer
( angle n cong angle m )
( angle r cong angle f )
( overline { n f } cong overline { h q } )
( overline { m n } cong overline { q r } )
( overline { q h } cong overline { m f } )
( angle m cong angle q )

Explanation:

Step1: Recall congruent triangle properties

When \(\triangle FMN\cong\triangle HQR\), corresponding angles and sides are congruent. That is \(\angle F\cong\angle H\), \(\angle M\cong\angle Q\), \(\angle N\cong\angle R\), \(\overline{FM}\cong\overline{HQ}\), \(\overline{MN}\cong\overline{QR}\), \(\overline{NF}\cong\overline{RH}\)

Step2: Analyze each option

• For \(\angle N\cong\angle M\): There is no information from \(\triangle FMN\cong\triangle HQR\) to support this. In \(\triangle FMN\), \(\angle N\) and \(\angle M\) are not necessarily congruent.
• For \(\angle R\cong\angle F\): Since \(\angle N\cong\angle R\) (from \(\triangle FMN\cong\triangle HQR\)) and \(\angle N

eq\angle F\) (in \(\triangle FMN\)), \(\angle R
ot\cong\angle F\)

• For \(\overline{NF}\cong\overline{HQ}\): \(\overline{NF}\cong\overline{RH}

eq\overline{HQ}\)

• For \(\overline{MN}\cong\overline{QR}\): By the congruence of \(\triangle FMN\cong\triangle HQR\), corresponding sides \(\overline{MN}\) and \(\overline{QR}\) are congruent.
• For \(\overline{QH}\cong\overline{MF}\): Since \(\overline{FM}\cong\overline{HQ}\), by the symmetric property of congruence \(\overline{QH}\cong\overline{MF}\)
• For \(\angle M\cong\angle Q\): By the congruence of \(\triangle FMN\cong\triangle HQR\), corresponding angles \(\angle M\) and \(\angle Q\) are congruent.

Answer:

\(\overline{MN}\cong\overline{QR}\), \(\overline{QH}\cong\overline{MF}\), \(\angle M\cong\angle Q\)