Question

1.

1. ∠3 ≅ ∠5

1.

1. ∠a and ∠b are supplementary.
2. ∠a ≅ ∠c;

∠a and ∠b are supplementary;
∠c and ∠d are supplementary.
2.

Explanation:

Step1: Analyze the first table

Since it is given that $\angle3\cong\angle5$ and the reason is “All right angles are congruent”, the first blank should be that $\angle3$ and $\angle5$ are right angles.

Step2: Analyze the second table

Given that $\angle A$ and $\angle B$ are supplementary, by the definition of supplementary angles (if two angles are supplementary, then the sum of their measures is $180^{\circ}$), we have $\angle A+\angle B = 180^{\circ}$.

Step3: Analyze the third table

We know that $\angle A\cong\angle C$, $\angle A$ and $\angle B$ are supplementary ($\angle A+\angle B=180^{\circ}$), $\angle C$ and $\angle D$ are supplementary ($\angle C+\angle D = 180^{\circ}$). Substituting $\angle A$ with $\angle C$ in $\angle A+\angle B=180^{\circ}$, we get $\angle C+\angle B=180^{\circ}$. Since $\angle C+\angle D = 180^{\circ}$, then $\angle B\cong\angle D$ (by the property that supplements of congruent angles are congruent).

Answer:

1. $\angle3$ and $\angle5$ are right angles.
2. $\angle A+\angle B = 180^{\circ}$
3. $\angle B\cong\angle D$