Question

Given: triangle ABC is an isosceles triangle with base AC

given: BD is perpendicular to AC

prove: triangle BDA is congruent to triangle BDC

I need a flow proof

Answer 1

To prove triangles BDA and BDC are congruent, one can use the properties of isosceles triangles and the SAS Postulate, considering the perpendicular bisector and the equal sides of the isosceles triangle.

Step-by-step explanation:

To prove that triangles BDA and BDC are congruent in an isosceles triangle ABC with base AC, and BD perpendicular to AC, a flow proof can be constructed using the properties of isosceles triangles and the definition of congruent triangles. As ABC is isosceles with AB equal to BC and BD is a perpendicular bisector to AC, we have two right triangles BDA and BDC.

1. Triangle ABC is isosceles, so AB is equal to BC.
2. BD is perpendicular to AC, creating right angles at D in triangles BDA and BDC.
3. Segment BD is common to both triangles BDA and BDC.
4. By the Reflexive Property, AD is equal to CD since BD is a bisector.
5. Since we have two sides and the included right angle equal, by the Side-Angle-Side (SAS) Postulate, triangle BDA is congruent to triangle BDC.

Through these steps, we establish the congruence of triangles BDA and BDC.