Aconjecture and the flowchart proof used to prove the conjecture are shown. drag an expression or phrase to each box to complete the proof.

1. (Box on the left): Given.

2. (Box on the right): Angle Addition Postulate.

3. °+°=∠DEF

4. Definition of right triangle.

5. ∠DEF is a right triangle.

Step-by-step explanation:

1. You have the angles given in the first figure.

2 and 3. The Angle Addition Postulate establishes that if GE is in the interior of the angle ∠DEF, then:

°+°=∠DEF

4. A rigth triangle is a triangle that has a angle of 90 degrees.

5. The angle ∠DEF measures 90 degrees, therefore, the triangle is a right triangle.

Blank 1: Given

Blank 2: Angle addition postulate

Blank 3:

Blank 4:

Blank 5: ∠DEF is a right angle.

Blank 6: Definition of right triangle

Step-by-step explanation:

Given: and .

Prove: ΔDEF is a right triangle.

Proof:

     (Given)

        (Angle addition postulate)

Substitute and in the above equation.

        (Substitution property of equality)

                 (On simplifying)

∠DEF is a right angle.                                    (Definition of right angle)

ΔDEF is a right triangle                        (Definition of right triangle)

Hence proved.

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step-by-step explanation: