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Setler79 [48]
3 years ago
15

A conjecture and the flowchart proof used to prove the conjecture are shown.

Mathematics
2 answers:
hodyreva [135]3 years ago
5 0

Answer:

1. (Box on the left): Given.

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

3. 51°+39°=m∠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:

51°+39°=m∠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.

aliya0001 [1]3 years ago
5 0

Answer:

Blank 1: Given

Blank 2: Angle addition postulate

Blank 3: 51^{\circ}+39^{\circ}=m\angle DE F

Blank 4: 90^{\circ}=m\angle DE F

Blank 5: ∠DEF is a right angle.

Blank 6: Definition of right triangle

Step-by-step explanation:

Given: m\angle DEG=51^{\circ} and m\angle GEF=39^{\circ}.

Prove: ΔDEF is a right triangle.

Proof:

m\angle DEG=51^{\circ},m\angle GEF=39^{\circ}      (Given)

m\angle DEG+m\angle GEF=m\angle DE F         (Angle addition postulate)

Substitute m\angle DEG=51^{\circ} and m\angle GEF=39^{\circ} in the above equation.

51^{\circ}+39^{\circ}=m\angle DE F         (Substitution property of equality)

90^{\circ}=m\angle DE F                  (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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