Question

Geometry math question no Guessing and Please show work

Answer 1

Let us consider the two triangles TPB and YSB

The figure shows < TPB = < YSB

The sides PB=SB

<TBP=<YBS( vertically opposite angles are equal)

Two angles and included side are equal in the triangles TPB and YSB.

If any two angles and the included side are the same in both triangles, then the triangles are congruent.

The two triangles are congruent by ASA property of congruence .

Option A is the right answer.

Answer 2

Consider the given triangles TPB and BSY,

PB=BS (Given )

`\angle TPB=\angle BSY` (Each angle is a right angle)

`\angle TBP=\angle SBY` (As vertically opposite angles are equal)

So, the given triangles are congruent by ASA postulate which states that "Triangles are congruent if any two angles and their included side are equal in both triangles".