D is a point on the base BC of an isosceltriangle ABC in which AB = AC

1.	D is a point on the base BC of an isosceltriangle ABC in which AB = AC. The trianADE is drawn such that AD - AE. D、LDA= LAC and D, E are on opposite sides ofArProve that(ii) triangles BAD and CAE are congruent(iii) AC bisects BCE.(SC
Answer» In triangle BAD and CAE AD=AE [given]AB=AC [given] We know that angle DAE=BACso the angle A of triangle ADC is common in both the angles. When we remove it we are left with angle BAD=CAE. Therefore the two triangles BAD and CAE are congruent by SAS TEST. Since AD = AE, AC will eventually bisect angle BCE

D is a point on the base BC of an isosceltriangle ABC in which AB = AC. The trianADE is drawn such that AD - AE. D、LDA= LAC and D, E are on opposite sides ofArProve that(ii) triangles BAD and CAE are congruent(iii) AC bisects BCE.(SC

Answer»

In triangle BAD and CAE

AD=AE [given]AB=AC [given]

We know that angle DAE=BACso the angle A of triangle ADC is common in both the angles.

When we remove it we are left with angle BAD=CAE.

Therefore the two triangles BAD and CAE are congruent by SAS TEST.

Since AD = AE, AC will eventually bisect angle BCE