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Class 9Class 10First YearSecond Year
$3. In the given figure we have \triangle A C E \cong \triangle B D E such that: m \overline{A C}=m \overline{B D}=3 \mathrm{~cm} \angle \mathrm{A}=(3 x+1)^{\circ} m \angle \mathrm{E}= (3 y-2)^{\circ} and m \angle \mathrm{B}=(x+35)^{\circ} . Find the values of x and y .$

$4. Find the value of unknowns for the given congruent triangles.$

$2. From a point on the line bisector of an angle perpendiculars are drawn to the arms of the angle. Prove that these perpendiculars are equal in measure.$

$1. \mathrm{ABC} is an isosceles triangle. \mathrm{D} is the mid-point of base \overline{\mathrm{BC}} . Prove that \overline{\mathrm{AD}} bisects \angle \mathrm{A} and \overrightarrow{\mathrm{AD}} \perp \overrightarrow{\mathrm{BC}} .$

$2. Prove that a point which is equidistant from the end points of a line segment is on the right bisector of the line segment.$

$3. Fill in the blanks to make the sentences true sentences:(vi) The sum of the measures of acute angle of a right triangle is$

$(iv) How many acute angles are there in an acute angled triangle?(a) 1(b) 2(c) 3(d) not more than 2 .$