Question

building builders use the king post truss, below left, for the top of a simple structure. in this truss, ( \triangle abc cong \triangle abd ). list the congruent corresponding parts.

Explanation:

Step1: Identify congruent angles

When \(\triangle ABC\cong\triangle ABD\), corresponding angles are congruent.
\(\angle ABC\cong\angle ABD\), \(\angle BAC\cong\angle BAD\), \(\angle ACB\cong\angle ADB\)

Step2: Identify congruent sides

Corresponding sides of congruent triangles are congruent.
\(AB = AB\) (common side), \(AC=AD\), \(BC = BD\)

Answer:

Congruent angles: \(\angle ABC\cong\angle ABD\), \(\angle BAC\cong\angle BAD\), \(\angle ACB\cong\angle ADB\)
Congruent sides: \(AB = AB\), \(AC=AD\), \(BC = BD\)