Question

Answer the questions with reference to the adjoining figure.



(1) Which triangles include points M and N?

(2) Which triangles have point E on their exterior?

(3) Which triangles have seg PS as a common side?

(4) Name the triangles in which ∠PTR is an exterior angle.

(5) Which triangles include points E, M and N?

(6) Of which triangles does ∠PSQ from an exterior angle?

(7) Which points in the figure are in the exterior of all triangles?

(8) Which points are outside ∆PQS but inside ∆PTR?

(9) Identify and name the exterior angles of ∆PST.

(10) List the triangles of which ∠PQS is an angle.

(11) Of which triangles is R a vertex?

(12) Which points lie outside ∆PST?

Answer 1

(1) The points M and N are inside ∆PST, ∆PQT, ∆PRS and ∆PQR.

(2) The point E is outside ∆PST, ∆PTR and ∆PSR.

(3) ∆PSQ & ∆PST, ∆PSQ & ∆PSR and ∆PSR & ∆PST have the segment PS as a common side.

(4) ∠PTR forms a linear pair with ∠PTS of ∆PST and ∠PTQ of ∆PTQ.
So, ∠PTR is an exterior angle of ∆PST and ∆PTQ.

(5) The points E, N and M lie inside ∆PQT and ∆PQR.

(6) ∠PSQ forms a linear pair with ∠PST of ∆PST and ∠PSR of ∆PSR.
Thus, ∠PSQ forms an exterior angle with the angles of ∆PST and ∆PSR.

(7) The points Y and Z lie outside all triangles.

(8) The point U lies inside ∆PTR and outside ∆PQS.

(9) Those angles which form a linear pair with the angles of a triangle are exterior angles for that triangle.
For ∆PST, ∠PSQ forms a linear pair with ∠PST.
So, ∠PSQ is an exterior angle.
∠PTR forms an exterior angle with ∠PTS.
So, ∠PTR is an exterior angle.
Thus, ∠PSQ and ∠PTR are exterior angles for ∆PST.

(10) ∠PQS is a common angle for ∆PQS, ∆PQT and ∆PQR.

(11) The following triangles have the point R as a vertex:
∆PRT, ∆PRS and ∆PRQ.

(12) The points E, U, Y, Q, R and Z lie outside ∆PST.