Question

17 multiple choice 5 points given the diagram below, which must be true? diagram of triangles with right angles, congruency marks options: δfxs ≅ δgxt, δxsf ≅ δxtg (selected), δfxs ≅ δxgt, δsxf ≅ δgxt

Explanation:

Step1: Analyze Markings

Check congruent segments (double/ triple bars) and right angles. \( SX = XG \) (double bars), \( FX = XT \) (x - marks), \( FS = GT \) (triple bars), \( \angle S = \angle G = 90^\circ \).

Step2: Identify Triangle Congruence

For \( \triangle XSF \) and \( \triangle XTG \): \( SX = XG \) (side), \( \angle S=\angle G = 90^\circ \) (angle), \( FX = XT \) (side). By SAS, \( \triangle XSF \cong \triangle XTG \) (matching vertex order \( X - S - F \) and \( X - T - G \)? Wait, no—wait the option is \( \triangle XSF \cong \triangle XTG \)? Wait the selected option is \( \triangle XSF \cong \triangle XTG \). Wait, let's check vertex correspondence. \( S \) corresponds to \( T \)? No, wait \( \angle S \) and \( \angle G \) are right angles. Wait, \( SX = XG \), \( FS = GT \), \( \angle S=\angle G \). So \( \triangle XSF \) (vertices X, S, F) and \( \triangle XTG \) (vertices X, T, G). Wait, actually, \( \triangle XSF \) and \( \triangle XTG \): \( SX = XG \), \( SF \) and \( TG \)? No, \( FS = GT \), \( \angle S = \angle G \). So by SAS, \( \triangle XSF \cong \triangle XTG \) (since \( SX = XG \), \( \angle S=\angle G \), \( FS = GT \)). So the correct option is \( \triangle XSF \cong \triangle XTG \).

Answer:

B. \( \triangle XSF \cong \triangle XTG \) (assuming the second option is labeled as B, with text \( \triangle XSF \cong \triangle XTG \))