Note: This is the Solution of review exercise 11 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Review Exercise 11
Question # 01: Four option are given against each statement. Encircle the correct option.
\((i)\) A triangle can be constructed if the sum of the measure of any two sides is ___________ the measure of the third side.
\( a) \quad \) less than
\( b) \quad \) greater than
\(c) \quad \) equal to
\( d) \quad \) greater than and equal to
\( \text{Answer/Explanation}\)
\((ii)\) An equilateral triangle__________
\( a) \quad \) can be isosceles
\( b) \quad \) can be right angled
\(c) \quad \) can be obtuse angled
\( d) \quad \) has each angle equal to \(50^\circ\)
\( \text{Answer/Explanation}\)
\((iii)\) If the sum of the measrues of two angles is less than \(90^\circ\), then the triangle is ___________
\( a) \quad \) equilateral
\( b) \quad \) acute angled
\(c) \quad \) obtuse angled
\( d) \quad \) right angled
\( \text{Answer/Explanation}\)
\((iv)\)\(\quad\)The line segment joining the midpoint of a side to its opposite vertex in a triangle is called_________
\( a) \quad \) median
\( b) \quad \) perpendicular bisector
\(c) \quad \) angle bisector
\( d) \quad \) circle
\( \text{Answer/Explanation}\)
\((v)\) \(\quad\)The angle bisectors of a triangle intersect at __________
\( a) \quad \) one point
\( b) \quad \) two points
\(c) \quad \) three points
\( d) \quad \) four points
\( \text{Answer/Explanation}\)
\((vi)\) \(\quad\) Locus of all points equidistant form a fixed point is __________
\( a) \quad \) circle
\( b) \quad \) perpendicular bisector
\(c) \quad \) angle bisector
\( d) \quad \) parallel lines
\( \text{Answer/Explanation}\)
\((vii)\)\(\quad\)Locus of points equidistant from two fixed points is__________
\( a) \quad \) circle
\( b) \quad \) perpendicular bisector
\(c) \quad \) angle bisector
\( d) \quad \) parallel lines
\( \text{Answer/Explanation}\)
\((viii)\)\(\quad\) Locus of points equidistant from a fixed line is/are______
\( a) \quad \) circle
\( b) \quad \) perpendicular bisector
\(c) \quad \) angle bisector
\( d) \quad \) parallel lines
\( \text{Answer/Explanation}\)
\((ix)\)\(\quad\)Locus of points equidistant from two intersecting lines is __________
\( a) \quad \) circle
\( b) \quad \) perpendicular bisector
\(c) \quad \) angle bisector
\( d) \quad \) parallel lines
\( \text{Answer/Explanation}\)
\((x)\) \(\quad\)The set of all points which is farther than \(2\ km\) from a fixed point \(B\) is a region outside a circle of radius _______ and center at \(B\).
\( a) \quad \) \(1\ km\)
\( b) \quad \) \(1.9\ km\)
\(c) \quad \) \(2\ km\)
\( d) \quad \) \(2.1\ km\)
\( \text{Answer/Explanation}\)
Question 2: Construct a right angled triangle with measures of sides \(\small{6\ cm}\), \(\small{8\ cm}\) and \(\small{10\ cm}\).
Question 3: Construct a triangle \(\small{ABC}\) with \(\small{m\overline{AB}=5.3\ cm}\), \(\small{m\angle A=30^\circ}\) and \(\small{m\angle B=1206\circ}\). Draw the locus of all points which are equidistant from \(\small{A}\) to \(\small{B}\).
Question 4: Construct a triangle with \(\small{m\overline{DE}=7.3\ cm}\), \(\small{m\angle D=42^\circ}\) and \(\small{m\overline{EF}=5.4\ cm}\).
Question 5: Construct a triangle \(\small{XYZ}\) with \(\small{m\overline{YX}=8\ cm}\), \(\small{m\overline{YZ}=7\ cm}\) and \(\small{m\overline{XZ}=6.5\ cm}\). Draw the locus of all points which are equidistant from \(\small{\overline{XY}}\) and \(\small{\overline{XZ}}\).
Question 6: Construct a triangle \(\small{FGH}\) such that \(\small{m\overline{FG}=m\overline{GH}=6.4\ cm}\), \(\small{m\angle G=122^\circ}\). Draw the locus of all point which are:
\( (a) \; \) equidistant from \(F\) and \(G\)
\( (b) \; \) equidistant from \(\overline{FG}\) and \(\overline{GH}\)
\( (c) \; \) Mark the point point where the two loci intersect.
Question 7: Two houses \(\small{Q}\) and \(\small{R}\) are \(\small{73}\) meters apart. Using a scale of \(\small{1\ cm}\) to represent \(\small{10\ m}\), construct the locus of a point \(\small{P}\) which moves such that it is:
\( (i) \; \) at a distance of \(\small{32}\) meters from \(\small{Q}\)
\( (ii) \; \) at a distance of \(\small{48}\) meters from the line joining \(\small{Q}\) and \(\small{R}\).