Question

Using Flowchart Proofs

Given: ∠ABC is a right angle and ∠DEF is a right angle.
Prove: All right angles are congruent by showing that ∠ABC ≅ ∠DEF.

Answer 1

To prove that all right angles are congruent, one can use a flowchart proof that leverages the definition of a right angle and the transitive property of equality to show that any two angles that measure 90 degrees are congruent.

Step-by-step explanation:

The question asks to prove that all right angles are congruent using flowchart proofs, given two specific right angles, ∠ABC and ∠DEF. A flowchart proof involves a sequence of statements and reasons that lead to a conclusion. Since all right angles measure 90 degrees by definition, any two right angles will be congruent.

Steps for a Flowchart Proof

Define the given information: ∠ABC and ∠DEF are right angles.

State a definition or theorem: Definition of a right angle - an angle that measures exactly 90 degrees.

Apply the definition to the given angles: ∠ABC measures 90 degrees and ∠DEF also measures 90 degrees.

Use the transitive property of equality: If two angles both measure 90 degrees, they must be equal in measure to each other.

Conclude: Therefore, ∠ABC ≅ ∠DEF because they both measure 90 degrees, making them congruent.

By following these steps, we establish the congruency of any two right angles through a flowchart proof.