Section 1
Regular Polygons
Tell whether each of the following statements is true or false.Every triangle is cyclic.
Tell whether each of the following statements is true or false.If a triangle is equilateral, it must be regular.
Tell whether each of the following statements is true or false.If a quadrilateral is equilateral, it must be regular.
Tell whether each of the following statements is true or false.If a quadrilateral is equiangular, it must be regular.
Tell whether each of the following statements is true or false.If a quadrilateral is equiangular, it must be cyclic.
Tell whether each of the following statements is true or false.If a polygon is regular, it must be convex.
Tell whether each of the following statements is true or false.If a polygon is regular, it must be cyclic.
Tell whether each of the following statements is true or false.If a polygon is cyclic, it must be regular.
Tell whether each of the following statements is true or false.If a polygon is regular, it must be equilateral.
Tell whether each of the following statements is true or false.If a polygon is equilateral, it must be equiangular.
Circle $\mathrm{O}$ is circumscribed about regular pentagon NITRE; $\overline{\mathrm{OG}} \perp \overline{\mathrm{RE}}$.(IMAGE CAN'T COPY)What is point O called with respect to the pentagon?
Circle $\mathrm{O}$ is circumscribed about regular pentagon NITRE; $\overline{\mathrm{OG}} \perp \overline{\mathrm{RE}}$.(IMAGE CAN'T COPY)What is $\overline{\mathrm{OG}}$ called?
Circle $\mathrm{O}$ is circumscribed about regular pentagon NITRE; $\overline{\mathrm{OG}} \perp \overline{\mathrm{RE}}$.(IMAGE CAN'T COPY)How do we know that $\overline{\text { OG }}$ bisects $\overline{\mathrm{RE}}$ ?
Circle $\mathrm{O}$ is circumscribed about regular pentagon NITRE; $\overline{\mathrm{OG}} \perp \overline{\mathrm{RE}}$.(IMAGE CAN'T COPY)What are $\overline{\mathrm{OR}}$ and $\overline{\mathrm{OE}}$ called with respect to NITRE?
Circle $\mathrm{O}$ is circumscribed about regular pentagon NITRE; $\overline{\mathrm{OG}} \perp \overline{\mathrm{RE}}$.(IMAGE CAN'T COPY)What kind of triangle is $\triangle O R E ?$
Circle $\mathrm{O}$ is circumscribed about regular pentagon NITRE; $\overline{\mathrm{OG}} \perp \overline{\mathrm{RE}}$.(IMAGE CAN'T COPY)What is $\underline{x}ROE$ called with respect to NITRE?
Circle $\mathrm{O}$ is circumscribed about regular pentagon NITRE; $\overline{\mathrm{OG}} \perp \overline{\mathrm{RE}}$.(IMAGE CAN'T COPY)Does $\overrightarrow{\mathrm{OG}}$ bisect $\underline{x}\mathrm{ROE} ?$
The figures below illustrate the central angles of some regular polygons.(IMAGE CAN'T COPY)As the number of sides of a regular polygon increases, how does the measure of one of its central angles change?
The figures below illustrate the central angles of some regular polygons.(IMAGE CAN'T COPY)Find the measure of a central angle of each figure shown.
The figures below illustrate the central angles of some regular polygons.(IMAGE CAN'T COPY)Find the measure of a central angle of a regular decagon.
The figures below illustrate the central angles of some regular polygons.(IMAGE CAN'T COPY)How would you express the measure of a central angle of a regular polygon that has $n$ sides in terms of $n ?$
The figure below suggests a way to construct a regular hexagon.(IMAGE CAN'T COPY)What kind of triangles surround point $O ?$
The figure below suggests a way to construct a regular hexagon.(IMAGE CAN'T COPY)How do the sides of the hexagon compare in length to the radius of the circle?
The figure below suggests a way to construct a regular hexagon.(IMAGE CAN'T COPY)Use your straightedge and compass to construct a regular hexagon by inscribing it in a circle.
The figure below suggests a way to construct a square.(IMAGE CAN'T COPY)What relation do $\overline{\mathrm{AC}}$ and $\overline{\mathrm{BD}}$ have to each other?
The figure below suggests a way to construct a square.(IMAGE CAN'T COPY)Use your straightedge and compass to construct a square by inscribing it in a circle.
The figure below suggests a way to construct a square.(IMAGE CAN'T COPY)Construct a regular octagon. (Hint: Begin by inscribing a square in a circle.)
The figure below suggests a way to construct a square.(IMAGE CAN'T COPY)Construct a regular dodecagon. (Hint: Begin by inscribing a regular hexagon in a circle.)
In the figure below, $\overline{\mathrm{OT}}$ is an apothem of regular pentagon KRYPN; $\angle \mathrm{O}=36^{\circ}$ and $\mathrm{ON}=10 .$ Use the appropriate trigonometric(IMAGE CAN'T COPY)$OT$
In the figure below, $\overline{\mathrm{OT}}$ is an apothem of regular pentagon KRYPN; $\angle \mathrm{O}=36^{\circ}$ and $\mathrm{ON}=10 .$ Use the appropriate trigonometric(IMAGE CAN'T COPY)$NT$
(IMAGE CAN'T COPY)Given: FLUORINE is a regular polygon with diagonals $\overline{\mathrm{NR}}$ and $\overline{\mathrm{RU}}$Prove: $ \mathrm{NR}=\mathrm{RU}$
(IMAGE CAN'T COPY)Given: $\mathrm{XYGEN}$ is a regular polygon with central angles 1 and 2Prove: $\angle 1=\angle 2$. (Hint: circumscribe circle $\mathrm{O}$ about XYGEN.)
(IMAGE CAN'T COPY)Given: CHLRINE is a regular polygon with center O. Prove: $\overrightarrow{\mathrm{LO}}$ bisects $\underline{x} \mathrm{HLR}$.
(IMAGE CAN'T COPY)Given: HELIUM is a regular hexagon with diagonals $\overline{\mathrm{HL}}$ and $\overline{\mathrm{MI}}$Prove: $\overline{\mathrm{HL}} \| \overline{\mathrm{MI}}$ without adding anything to the figure.