Question

statement reason
1 ∠4 and ∠7 form a linear pair given
2 ∠4 and ∠7 are supplementary reflexive property transitive property substitution property
3 ∠4 ≅ ∠6 definition of congruent angles angle addition property
4 ∠7 ≅ ∠6 definition of supplementary angles
5 ∠□ ≅ ∠□ definition of complementary angles definition of linear pair
6 ∠4 and ∠7 are right angles select

Explanation:

Step1: Use the definition of linear pair

By the definition of a linear pair, if two angles form a linear pair, then they are supplementary. Since $\angle4$ and $\angle7$ form a linear pair (given), so $\angle4$ and $\angle7$ are supplementary.

Step2: Use the property of congruent angles

Given $\angle4\cong\angle6$, and from step 1 we know $\angle4+\angle7 = 180^{\circ}$. Substituting $\angle4$ with $\angle6$ (substitution property), we get $\angle6+\angle7=180^{\circ}$. Also, since $\angle7\cong\angle6$ (from step 4, assume we have shown that they are congruent through some angle - related properties like vertical angles or other angle - pair relationships in a geometric figure), and if two congruent angles are supplementary ($\angle6+\angle7 = 180^{\circ}$), then each angle is a right angle.

Answer:

For statement 2, the reason is "Definition of Linear Pair". For statement 4, if we assume a geometric figure where $\angle7$ and $\angle6$ are vertical angles (a common case in angle - pair problems in geometry), the reason for $\angle7\cong\angle6$ could be "Vertical Angles Theorem". For statement 6, if two supplementary angles ($\angle4$ and $\angle7$) are congruent (from previous steps of showing $\angle4\cong\angle6$ and $\angle7\cong\angle6$ so $\angle4\cong\angle7$), then $\angle4$ and $\angle7$ are right angles. The reason for statement 6 is "If two congruent angles are supplementary, then each is a right angle".