Question

Building builders use the king post truss, below left, for the top of a simple structure. In this truss, increment a b c space approximately equal to space increment a b d. List the congruent corresponding parts.

a) AB = BD
b) AC = DC
c) BC = CD
d) AD = AD

Answer 1

In a king post truss, if ∆ABC is approximately equal to ∆ABD, then the congruent corresponding parts are AB = BD, AC = DC, BC = CD, and AD = AD.

Step-by-step explanation:

The student's question relates to the properties of a king post truss, which is a structure commonly used in the construction of roofs. In the given truss, if we are given that segments AB and BD are approximately equal (∆ABC ≈ ∆ABD), then the corresponding congruent parts based on this information would be:

• AB = BD (Given, as stated in the question)
• AC = DC (congruent parts in corresponding positions if ∆ABC ≈ ∆ABD)
• BC = CD (congruent parts in corresponding positions if ∆ABC ≈ ∆ABD)
• AD = AD (Common side to both triangles)

Because the two triangles share a side, AD, and AB is congruent to BD, the remaining sides and angles of these triangles would also be congruent by the Side-Angle-Side (SAS) congruence postulate if there is a congruent angle between the two congruent sides.