Question

Line SU bisects angle RST. Which statement is NOT true?

A) ∠RST = ∠RSU
B) ∠RSU = ∠UST
C) ∠SQU = ∠SPU
D) PS = QS

Answer 1

Answer : The incorrect option is, (A) ∠RST = ∠RSU

Step-by-step explanation :

As we are given that, line SU bisects angle RST and SPUQ is a rhombus.

First we have to determine that ΔSQU and ΔSPU are congruent triangles.

Proof:

Side SU = Side SU (common side)

∠SQU = ∠SPU (In rhombus opposite angle are always equal)

∠RSU = ∠UST (angle bisector)

ΔSQU ≅ ΔSPU (By ASA congruency)

So, Side PS = Side QS

∠RST = ∠RSU this option is wrong because
`\angle RSU=(1)/(2)\angle RST`

Thus, the incorrect option is, (A) ∠RST = ∠RSU

Answer 2

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
so the answer is B