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Class 9Class 10First YearSecond Year
$EXERCISE 10.4 1. In \triangle \mathrm{PAB} of figure \overline{\mathrm{PQ}} \perp \overline{\mathrm{AB}} and \overline{\mathrm{PA}} \cong \overline{\mathrm{PB}} prove that \overline{\mathrm{AQ}} \cong \overline{\mathrm{BQ}} and \angle \mathrm{APQ} \cong \angle \mathrm{BPQ} .$  $4. Find the value of unknowns for the given congruent triangles.$  $2. From a point on the line bisector of an angle perpendiculars are drawn to the arms of the angle. Prove that these perpendiculars are equal in measure.$  $1. \mathrm{ABC} is an isosceles triangle. \mathrm{D} is the mid-point of base \overline{\mathrm{BC}} . Prove that \overline{\mathrm{AD}} bisects \angle \mathrm{A} and \overrightarrow{\mathrm{AD}} \perp \overrightarrow{\mathrm{BC}} .$  $2. Prove that a point which is equidistant from the end points of a line segment is on the right bisector of the line segment.$  $3. Fill in the blanks to make the sentences true sentences:(vi) The sum of the measures of acute angle of a right triangle is$  $(iv) How many acute angles are there in an acute angled triangle?(a) 1(b) 2(c) 3(d) not more than 2 .$  