Knowing that ∠ C≌ ∠ OTU and ∠ U≌ ∠ U, we can prove that △ SCU is similar to △ OTU. So we have \(\frac { OU} { SU} = \frac { TU} { CU} \), which tells us SU=15. So ST=15-4=11.

Supplemental Knowledge

In geometry, similar triangles are triangles that have the same shape but may differ in size. This means they have equal corresponding angles and proportional corresponding sides.

1. Angle-Angle (AA) Similarity Postulate:
   • If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
2. Proportional Sides:
   • In similar triangles, the ratios of the lengths of corresponding sides are equal.

Real-Life Connections

• Understanding similar triangles is useful in various fields such as architecture, engineering, and even art. For example, architects use principles of similar triangles to create scale models of buildings. Engineers use them to determine heights and distances that are otherwise difficult to measure directly.

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