Note: This is the Solution of review exercise 11.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 11.1
Question # 01: Construct \(\small{\triangle ABC}\) with the given measurements and verify that the perpendicular bisectors of the triangle are concurrent.
\( (i) \; \) \(m\overline{AB}=5\ cm\), \(m\overline{BC}=6\ cm\) and \(m\overline{AC}=7\ cm\)
\( (ii) \; \) \(m\overline{AB}=7.1\ cm\), \(m\angle{B}=135^\circ\) and \(m\overline{BC}=6.5\ cm\)
Question 2: Construct \(\small{\triangle LMN}\) of the following measurements and verify that the medians of the triangle are concurrent.
\( (i) \; \) \(m\overline{LM}=4.9\ cm\), \(m\angle{L}=51^\circ\) and \(m\angle{M}=8.1^\circ\)
\( (ii) \; \) \(m\overline{MN}=4.8\ cm\), \(m\angle{N}=30^\circ\) and \(m\overline{LM}=8.1\ cm\)
Question 3: Verify that the angle bisectors of \(\small{\triangle ABC}\) are concurrent with the following measurement:
\( (i) \; \) \(m\overline{AB}=4.5\ cm\), \(m\angle{A}=45^\circ\) and \(m\overline{AC}=5.3\ cm\)
\( (ii) \; \) \(m\overline{AB}=6\ cm\), \(m\angle{A}=150^\circ\) and \(m\angle{B}=60^\circ\)
Question 4: Given measurements of \(\small{\triangle DEF}\): \(\small{m\overline{DE}=4.8\ cm}\), \(\small{m\overline{EF}=4\ cm}\) and \(\small{m\angle{E}=45^\circ}\), draw altitudes of \(\small{\triangle DEF}\) and find orthocenter.
Question 5: Construct the following triangles and find whether there exists any ambiguous case.
\( (i) \; \) \(\triangle BCD;\)\(m\overline{BC}=5\ cm\), \(m\angle{B}=62^\circ\) and \(m\overline{CD}=4.7\ cm\)
\( (ii) \; \) \(\triangle KLM;\) \(m\overline{LM}=6\ cm\), \(m\angle{M}=42^\circ\) and \(m\overline{LN}=5\ cm\)