Asked by Seaira
Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary? (1 point)
Quadrilateral CDEF is inscribed in circle A.
Quadrilateral CDEF is inscribed in circle A, so m arc CDE+ m arc CFE= 360°. ∠CFE and ∠CDE are _________________, which means that their measures are one half the measure of their intercepted arcs. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2 ⋅ m∠CDE. Using the _________________, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.
inscribed angles; substitution property of equality
central angles; substitution property of equality
inscribed angles; addition property of equality
central angles; addition property of equality
Quadrilateral CDEF is inscribed in circle A.
Quadrilateral CDEF is inscribed in circle A, so m arc CDE+ m arc CFE= 360°. ∠CFE and ∠CDE are _________________, which means that their measures are one half the measure of their intercepted arcs. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2 ⋅ m∠CDE. Using the _________________, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.
inscribed angles; substitution property of equality
central angles; substitution property of equality
inscribed angles; addition property of equality
central angles; addition property of equality
Answers
Answered by
GPT-4o mini
The correct statements that complete the proof are:
**inscribed angles; addition property of equality**
So, the completed proof would read:
Quadrilateral CDEF is inscribed in circle A.
Quadrilateral CDEF is inscribed in circle A, so m arc CDE + m arc CFE = 360°. ∠CFE and ∠CDE are **inscribed angles**, which means that their measures are one half the measure of their intercepted arcs. So, m arc CDE = 2 ⋅ m∠CFE and m arc CFE = 2 ⋅ m∠CDE. Using the **addition property of equality**, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.
**inscribed angles; addition property of equality**
So, the completed proof would read:
Quadrilateral CDEF is inscribed in circle A.
Quadrilateral CDEF is inscribed in circle A, so m arc CDE + m arc CFE = 360°. ∠CFE and ∠CDE are **inscribed angles**, which means that their measures are one half the measure of their intercepted arcs. So, m arc CDE = 2 ⋅ m∠CFE and m arc CFE = 2 ⋅ m∠CDE. Using the **addition property of equality**, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.