Question

triangle fgh and triangle fbh are drawn below. if $overline{fh}congoverline{fh}$, $angle ghfcongangle bhf$, and $angle hfgcongangle hfb$, use the dropdown boxes below to determine a transformation that maps triangle fgh onto triangle fbh. then use a congruence statement to explain why this is possible.

Explanation:

Step1: Identify the transformation

Since $\overline{FH}\cong\overline{FH}$, $\angle GHF\cong\angle BHF$, and $\angle HFG\cong\angle HFB$, the line $FH$ is the axis of symmetry. The transformation that maps $\triangle FGH$ onto $\triangle FBH$ is a reflection over the line $FH$.

Step2: Write the congruence statement

By the Angle - Side - Angle (ASA) congruence criterion, because we have a common side $\overline{FH}$, and two pairs of congruent angles ($\angle GHF\cong\angle BHF$ and $\angle HFG\cong\angle HFB$), we can say that $\triangle FGH\cong\triangle FBH$.

Answer:

The transformation is a reflection over the line $FH$. The congruence statement is $\triangle FGH\cong\triangle FBH$ by ASA.