Q In the equilateral triangle ABC, AD and BE are the medians on the sides BC and CA respectively - Maths - Congruence of Triangles

Question

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

Shruti Tyagi · Accepted Answer

Dear student, Question 11)

In ∆PQM and ∆PRMPQ=PR --(given)QM=RM --(given)PM=PM --(common)∴∆PQM≅∆PRM (by SSS property)⇒∠PQM=∠PRM --(CPCT)Hence proved Question 12)

Since AD is bisector of ∠A⇒∠BAD=∠CAD (1)In ∆ADB and ∆ADC∠BAD=∠CAD --[from (1)]AD=AD --(common)∠ADB=∠ADC --(each 90°)∴∆ADB≅∆ADC --(by ASA property)⇒AB=AC --(CPCT)Thus, ∆ABC is an issosceles triangle Regards