Q. In the equilateral triangle ABC, AD and BE are the medians on the sides BC and CA respectively. Show that AD =  BE. 
10) In triangle ABC, AB = AC.BC and CB 
are extended to E and D respectively such 
that CE =BD Prove that AD = AE 
13) AABC is an isosceles triangle in which AB=AC. E and F are the midpoints of AB and AC respectively. Show that CE = BE. 
14) Triangle PQR is an isosceles 
triangle in which PQ=PR. O is a point 
such that QO = RO. Prove that PO bisects 
angle QPR. 
15) Triangle ABC is an isosceles triangle with AB=AC- Prove that the bisector of 
angle A divides triangle ABC into tvvo congruent triangles. 

Dear student,

Question 11)

In PQM and PRMPQ=PR --(given)QM=RM --(given)PM=PM  --(common)PQMPRM  (by SSS property)PQM=PRM  --(CPCT)Hence proved

Question 12)

Since AD is bisector of ABAD=CAD ...(1)In ADB and ADCBAD=CAD  --[from (1)]AD=AD --(common)ADB=ADC --(each 90°)ADBADC --(by ASA property)AB=AC  --(CPCT)Thus, ABC is an issosceles triangle

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