Question

reflect (drag the icon to indicate your level of understanding). \today i will understand the relationships between interior angle exterior angles in a triangle.\ im lost ——————————————————————————————— i got it think (complete the problem. draw on paper and take a picture or use digital tools.) prove corollary 4. include a given and prove statement, a diagram and a two - column proof. corollary 4 the acute angles of a right triangle are complementary.

Explanation:

Step1: State the Given

Given: $\triangle ABC$ is a right - triangle with $\angle C = 90^{\circ}$.

Step2: Recall the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, in $\triangle ABC$, $\angle A+\angle B+\angle C=180^{\circ}$.

Step3: Substitute the value of $\angle C$

Since $\angle C = 90^{\circ}$, we have $\angle A+\angle B + 90^{\circ}=180^{\circ}$.

Step4: Solve for $\angle A+\angle B$

Subtract $90^{\circ}$ from both sides of the equation: $\angle A+\angle B=180^{\circ}-90^{\circ}=90^{\circ}$.

Step5: Define complementary angles

Two angles are complementary if the sum of their measures is $90^{\circ}$. Since $\angle A+\angle B = 90^{\circ}$, $\angle A$ and $\angle B$ are complementary.

Answer:

The proof is as follows:

Statements	Reasons
2. $\angle A+\angle B+\angle C=180^{\circ}$	Angle - sum property of a triangle
3. $\angle A+\angle B + 90^{\circ}=180^{\circ}$	Substitution ($\angle C = 90^{\circ}$)
4. $\angle A+\angle B=90^{\circ}$	Subtraction property of equality
5. $\angle A$ and $\angle B$ are complementary	Definition of complementary angles