Question

vocabulary
flow - chart proof, or flow proof, p. 168
paragraph proof or narrative proof, p. 171
study tip
when you prove a theorem, write the hypothesis of the theorem as the given statement. the conclusion is what you must prove.
writing flowchart proofs
another proof format is a flowchart proof, or flow proof, which uses boxes and arrows to show the flow of a logical argument. each reason is below the statement it justifies. a flowchart proof of the right angles congruence theorem is shown in example 1.
theorem
2.3 right angles congruence theorem
all right angles are congruent.
example 1
proving the right angles congruence theorem
use the given flowchart proof to write a two - column proof of the right angles congruence theorem.
given ∠1 and ∠2 are right angles.
prove ∠1≅∠2
flowchart proof
∠1 and ∠2 are right angles. given
m∠1 = 90°, m∠2 = 90° definition of right angle
m∠1=m∠2 transitive property of equality
∠1≅∠2 definition of congruent angles
two - column proof
statements\treasons

1. ∠1 and ∠2 are right angles.\t1. given
2. m∠1 = 90°, m∠2 = 90°\t2. definition of right angle
3. m∠1=m∠2\t3. transitive property of equality
4. ∠1≅∠2\t4. definition of congruent angles

Explanation:

Step1: State given information

Given that $\angle1$ and $\angle2$ are right - angles.

Step2: Apply right - angle definition

By the definition of a right - angle, $m\angle1 = 90^{\circ}$ and $m\angle2=90^{\circ}$.

Step3: Use transitive property

Since $m\angle1 = 90^{\circ}$ and $m\angle2 = 90^{\circ}$, by the transitive property of equality, $m\angle1=m\angle2$.

Step4: Apply congruent - angle definition

By the definition of congruent angles (if $m\angle A=m\angle B$, then $\angle A\cong\angle B$), $\angle1\cong\angle2$.

Answer:

The proof that if $\angle1$ and $\angle2$ are right angles then $\angle1\cong\angle2$ is completed as shown above.