Question

what values of s and t make δefg ≅ δbcd?
(images of two right triangles: δefg with right angle at g, leg s, hypotenuse 40; δbcd with right angle at d, leg 14, hypotenuse t)
s =
t =

Explanation:

Step1: Identify corresponding sides in congruent triangles

Since \(\triangle EFG \cong \triangle BCD\), their corresponding sides are equal. In right triangles, the right - angled sides and hypotenuses correspond. For \(\triangle EFG\) (right - angled at \(G\)) and \(\triangle BCD\) (right - angled at \(D\)), the side \(s\) in \(\triangle EFG\) corresponds to side \(BD = 14\) in \(\triangle BCD\), and the side \(t\) in \(\triangle BCD\) corresponds to side \(EF=40\) in \(\triangle EFG\).

Step2: Determine the values of \(s\) and \(t\)

From the correspondence of congruent triangles:

• For \(s\): Since the side with length \(s\) in \(\triangle EFG\) corresponds to the side with length \(14\) in \(\triangle BCD\) (because \(\triangle EFG\cong\triangle BCD\) and the right - angled sides are corresponding), we have \(s = 14\).
• For \(t\): Since the side with length \(t\) in \(\triangle BCD\) corresponds to the side with length \(40\) in \(\triangle EFG\) (because \(\triangle EFG\cong\triangle BCD\) and the hypotenuses are corresponding), we have \(t = 40\).

Answer:

\(s=\boldsymbol{14}\), \(t=\boldsymbol{40}\)