Question

in the diagram below, $\angle rst \cong \angle uvt$. enter segments in the blanks provided that would result in a true equation.

(diagram of two triangles intersecting at point t, with vertices u, v, t and r, s, t)

answer attempt 1 out of 2
$\dfrac{rt}{rs} = \dfrac{\boxed{}}{\boxed{}}$

Explanation:

Step1: Identify Similar Triangles

Given \( \angle RST \cong \angle UVT \) and \( \angle RTS \cong \angle UTV \) (vertical angles), triangles \( \triangle RST \) and \( \triangle UVT \) are similar by AA (Angle - Angle) similarity criterion.

Step2: Corresponding Sides in Similar Triangles

In similar triangles, the ratios of corresponding sides are equal. For \( \triangle RST \sim \triangle UVT \), the corresponding sides are \( RT \) and \( UT \), \( RS \) and \( UV \), \( ST \) and \( VT \). So, from the ratio \( \frac{RT}{RS} \), the corresponding ratio in \( \triangle UVT \) would be \( \frac{UT}{UV} \).

Answer:

\(\frac{UT}{UV}\)