Question

III. Supply the reasons that correspond to the given statement in order to complete the proof of the theorem. Theorem: Each diagonal of a rhombus bisects opposite angles. Given: \boxed{FREN} is a rhombus Prove: \angle 1 \cong \angle 2 \angle 3 \cong \angle 4 F R Statements Reasons 1.Parallelogram FREN is a rhombus. 1. 2. \overline{FN} \cong \overline{FR}; \overline{RE} \cong \overline{EN} 2. 3. \overline{NR} \cong \overline{RN} 3. 4. \triangle NFR \cong \triangle REN 4. 5. \angle 1 \cong \angle 2 5. \angle 3 \cong \angle 4 E N

          III.
Supply the reasons that correspond to the given statement in order to complete the
proof of the theorem.
Theorem: Each diagonal of a rhombus bisects opposite angles.
Given: \boxed{FREN} is a rhombus
Prove: \angle 1 \cong \angle 2
\angle 3 \cong \angle 4
F
R
Statements
Reasons
1.Parallelogram FREN is a rhombus.
1.
2. \overline{FN} \cong \overline{FR}; \overline{RE} \cong \overline{EN}
2.
3. \overline{NR} \cong \overline{RN}
3.
4. \triangle NFR \cong \triangle REN
4.
5. \angle 1 \cong \angle 2
5.
\angle 3 \cong \angle 4
E
N

III.
Supply the reasons that correspond to the given statement in order to complete the
proof of the theorem.
Theorem: Each diagonal of a rhombus bisects opposite angles.
Given: FREN is a rhombus
Prove: ∠1 ≅∠2
∠3 ≅∠4
F
R
Statements
Reasons
1.Parallelogram FREN is a rhombus.
1.
2. FN ≅FR; RE ≅EN
2.
3. NR ≅RN
3.
4. NFR ≅REN
4.
5. ∠1 ≅∠2
5.
∠3 ≅∠4
E
N

Added by Scott C.

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