Question

Plz explain and prove the triangles congruence.

Answer 1

The explanation is given below with the diagram.

Explanation:

Given:

Δ ABC is an Isosceles triangle with base AB.

D is the midpoint of AB

∴ AD = BD

To Prove:

`\angle ACD \cong \angle BCD`

Proof:

Isosceles triangle property:

If Δ ABC is an Isosceles triangle with base AB, then the two sides are congruent and the base angles are congruent.

`\therefore \overline{AC} \cong \overline {BC}\ and\\\therefore \angle CAD} \cong \angle CBD`

`In\ \triangle ACD\ and\ \triangle BCD\\\overline{AC} \cong \overline{BC}\ \textrm{ Two sides of Isosceles Triangle are congruent}\\\angle CAD \cong \angle CBD\ \textrm{Base angles of Isosceles Triangle are congruent }\\\overline{AD} \cong \overline{BD}\ \textrm{ D is the midpoint of AB given}\\\therefore \triangle ACD \cong \triangle BCD\ \textrm{ By Side-Angle-Side test}\\\therefore \angle ACD \cong \angle BCD\ \textrm{corresponding parts(angles) of congruent triangles}\\`

`\therefore \angle ACD \cong \angle BCD\ \textrm{ Proved}`