A student draws a triangle that is acute-angled or obtuse-angled but not right-angled.
The student counts the number of straight lines that divide the triangle into two triangles, at least one of which is right-angled.
Which of the following statements is/are true?
I The student can draw a triangle for which there is exactly 1 such straight line.
II The student can draw a triangle for which there are exactly 2 such straight lines.
III The student can draw a triangle for which there are exactly 3 such straight lines.
- Anone of them
- BI only
- CII only
- DIII only
- EI and II only
- FI and III only
- GII and III only
- HI, II and III
Show the answer and worked solution
answer · D
- Anone of them
- BI only
- CII only
- DIII only
- EI and II only
- FI and III only
- GII and III only
- HI, II and III
Any line splitting a triangle into two triangles runs from a vertex to the opposite side. The right angle can sit at the foot of that line, or at the vertex it leaves from. If the triangle is acute, all three altitudes have their feet inside the opposite side and no vertex angle exceeds 90∘, giving exactly 3 lines. If it is obtuse at A, the altitudes from the two acute vertices land outside, leaving only the altitude from A — but the angle at A exceeds 90∘, so two further lines from A meet AB and AC at right angles, again giving 3. The count is always 3.