tmua 2023 Q8

tmua · Uk · paper2 1 marks Proof True/False Justification
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.
A none of them B I only C II only D III only E I and II only F I and III only G II and III only H I, II and III
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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.

A none of them
B I only
C II only
D III only
E I and II only
F I and III only
G II and III only
H I, II and III