Question

c.6 angle bisectors
what is ( ru )?
diagram: triangle with vertex ( s ), ( r ) and ( t ) on sides (right angles at ( r ) and ( t )), ( ut = 56 ), ( u ) below ( s ). ( ru = square )

Explanation:

Step1: Identify the theorem

We use the Angle - Bisector Theorem for right - angled triangles. If a point lies on the angle bisector of an angle, then it is equidistant from the two sides of the angle. In this figure, \(SU\) is the angle bisector of \(\angle RST\), and \(UR\perp SR\), \(UT\perp ST\). So, by the angle - bisector property, \(RU = TU\).

Step2: Determine the length of \(RU\)

We are given that \(TU = 56\). Since \(RU=TU\) (from the angle - bisector property), we can conclude that \(RU = 56\).

Answer:

\(56\)