Question

(b) problem 13: (first taught in lesson 23)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: ∠apj ≅ ∠lpj, ∠apj and ∠lpj are a linear pair.
prove: ∠apj and ∠lpj are right angles.

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, i.e., $\angle APJ+\angle LPJ = 180^{\circ}$ since they are a linear pair.

Step2: Use congruence property

Given $\angle APJ\cong\angle LPJ$, so $\angle APJ=\angle LPJ$. Let $\angle APJ = x$ and $\angle LPJ=x$. Then $x + x=180^{\circ}$ (from step 1).

Step3: Solve for the angle measure

Combining like terms gives $2x = 180^{\circ}$. Dividing both sides by 2, we get $x = 90^{\circ}$. So $\angle APJ$ and $\angle LPJ$ are right angles.

Answer:

The definition of a linear - pair of angles and the fact that congruent angles in a linear pair are right angles justify the prove statement.