(2) each interior angle i equals
(3) each exterior angle e equals
.
p. 156 - Frame 1 - The area of a rectangle equals the product of its base and altitude.
p. 157 - Frame 3 - The area of a parallelogram equals the product of a side and the altitude to that side.
p. 158 - Frame 4 - The area of a triangle equals one-half the product of a side and the altitude to that side.
p. 159 - Frame 5 - The area of a trapezoid equals one-half the product of its altitude and the sum of its bases. (The area of a trapezoid equals the product of its altitude and median.
p. 160 - Frame 7
| Pr. 1 | Parallelograms have equal areas if they have congruent bases and congruent altitudes. | Proof - Not given |
| Pr. 2 | Triangles have equal areas if they have congruent bases and congruent altitudes. | Proof - Not given |
| Pr. 3 | A median divides a triangle into two triangles of equal area. | Student exercise |
| Pr. 4 | Triangles have equal area if they have a common base and their vertices lie on a line parallel to the base. | Proof - Not given |
p. 165 - Frame 8
| Pr. 1 | If a regular polygon of n sides has a side s, the perimeter is p = ns. | Proof - Not given |
| Pr. 2 | A circle may be circumscribed about any regular polygon. | Proof - Not given |
| Pr. 3 | A circle may be inscribed in any regular polygon. | Proof - Not given |
| Pr. 4 | The center of the circumscribed circle of a regular polygon is also the center of its inscribed circle. | Definition |
| Pr. 5 | An equilateral polygon inscribed in a circle is a regular polygon. | Proof - Student Exercise |
| Pr. 6 | Radii of a regular polygon are congruent. | Proof - Not given |
| Pr. 7 | A radius of a regular polygon bisects the angle to which it is drawn. | Proof - Student Exercise |
| Pr. 8 | Apothems of a regular polygon are congruent. | Proof - Not given |
| Pr. 9 | An apothem of a regular polygon bisects the side to which it is drawn. | Proof - Student Exercise |
| Pr. 10 | For a regular polygon of n sides: (1) each central
angle c equals
(2) each interior angle i equals
(3) each exterior angle e equals
. |
Proof - Student Exercise |
p. 167 - Frame 9 - The area of a regular polygon equals one-half the product of its perimeter and apothem.
p. 169 - Frames 12-14
| Pr. 1 | In a circle of radius r, the length l of an arc of
n° equals
of the circumference of the circle, or
 . |
Proof - Not given |
| Pr. 2 | In a circle of radius r, the area K of a
sector of n° equals
of
the area of the circle, or
 . |
Proof - Not given |
| Pr. 3 |
 |
Proof - Student Exercise |
| Pr. 4 | The area of a minor segment of a circle equals the area of its sector less the area of the triangle formed by its radii and chord. | Proof - Not given |
p. 174 - Frame 15
| Pr. 1 | The locus of a point equidistant from two given points is the perpendicular bisector of the line segment joining the two points. | Proof - Not given |
| Pr. 2 | The locus of a point equidistant from two given parallel lines is a line parallel to the two lines and midway between them. | Proof - Not given |
| Pr. 3 | The locus of a point equidistant from the sides of a given angle is the bisector of the angle. | Proof - Not given |
| Pr. 4 | The locus of a point equidistant from two given intersecting lines is the bisectors of the angles formed by the lines. | Proof - Not given |
| Pr. 5 | The locus of a point equidistant from two concentric circles is the circle concentric with the given circles and midway between them. | Proof - Not given |
| Pr. 6 | The locus of a point a given distance from a given point is a circle whose center is the given point and whose radius is the given distance. | Proof - Not given |
| Pr. 7 | The locus of a point at a given distance from a given line is a pair of lines, parallel to the given line and at the given distance from the given line. | Proof - Not given |
| Pr. 8 | The locus of a point at a given distance from a given circle whose radius is greater than that distance is a pair of concentric circles, one on either side of the given circle and at the given distance from it. | Proof - Not given |
| Pr. 9 | The locus of a point at a given distance from a given circle whose radius is less than the distance, is a circle outside the given circle and concentric to it. Note: If r = d, the locus also includes the center of the given circle. | Proof - Not given |
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