Q. 75.0( 1 Vote )

# State giving reasons, whether the following statements are true or false: In all the following questions the line does not contain a side of the triangle.(1) A line can be drawn in the plane of a triangle not intersecting any of the sides of a triangle.(2) A line can be drawn in the plane of a triangle which is not passing through any of the three vertices and intersecting all the three sides of the triangle.(3) If a line drawn in the plane of a triangle intersects the triangle at only one point, the line passes through a vertex of the triangle.(4) If a line intersects two of the three sides of a triangle in two distinct points and does not intersect the third side, then the line is parallel to the third side.(5) In the plane of Δ ABC, a line / can be drawn such that = {P}, = {Q} and = ϕ.

(1) The given statement is true because for a line in the plane of a Δ, there are 3 possibilities

i) The line does not intersect the Δ

ii) The line intersects the Δ at one point

iii) The line intersects the Δ at two points

The first possibility is satisfied; hence the given statement is true. (2) The given statement is false because according to the theorem, if a line lying in the plane of a Δ and not passing through any vertex intersects one side, then it does intersect one more side but does not intersect the third side. Thus, a line not passing through a vertex of a Δ cannot intersect all the three sides.

(3) The given statement is true because a line intersecting a Δ and not passing through any vertex will intersect the Δ at two points. (4) The given statement is false because if a line intersects two sides of a Δ and does not intersect the third side, it can intersect the line containing the third side. (5) The given statement is true because in the plane of ΔABC, if line l intersects and at distinct points P and Q respectively, then according to the theorem, if a line lying in the plane of a Δ and not passing through any vertex intersects one side, then it does intersect one more side but does not intersect the third side, it cannot intersect .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Basic Proportionality Theorem42 mins  Champ Quiz | Thales Theorem49 mins  Quiz | Criterion of Similarity of Triangle45 mins  NCERT | Strong Your Basics of Triangles39 mins  RD Sharma | Imp. Qs From Triangles41 mins  R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class  How to Ace Maths in NTSE 2020?36 mins  R.D Sharma | Solve Exercise-4.545 mins  NCERT | Basic Proportionality Theorem22 mins  RD Sharma | Imp Qs Discussion- Triangles43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 