Question

Given AC is the angle bisector of ZBAD, prove AABC AADC by filling out the flowchart below.

Type of Statement
Type of Statement
Reason:
↓
D
For each box, choose a statement format from the dropdown menu. You will then be able to change the letters to match the diagram for this problem.
Reason:
A
Type of Statement
Reason:
↓
Type of Statement
Reason:
a
12
Type of Statement
8
Reason:
COP

Answer 1

∆ABC ≅ ∆ADC (Angle-Angle-Side ASA)

What are the criteria for congruence of triangles?

Proving congruence involves demonstrating that corresponding sides and angles of two triangles are equal, satisfying specific congruence criteria.

The criteria for congruence of triangles include Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL).

These conditions ensure that two triangles are congruent, meaning they have equal sides and angles.

∆ABC and ∆ADC ( To prove that they are congruent)

m∠D = m∠B (Given)

AC = AC (Reflective property postulate)

m∠CAD = m∠BAC ( AC bisects ∠BAD)

∆ABC ≅ ∆ADC (Angle-Angle-Side ASA)