p. 111 - Frame 2
| Pr. 1 | A diameter divides a circle into two congruent parts. | Proof - Not given |
| Pr. 2 | If a chord divides a circle into two congruent parts, then it is a diameter. | Proof - Not given |
| Pr. 3 | A point is outside, on, or inside a circle according to whether its distance from the center is greater than, equal to, or less than the radius. | Definition |
| Pr. 4 | Radii of the same or congruent circles are congruent. | Definition |
| Pr. 5 | Diameters of the same or congruent circles are congruent. | Proof - Student Exercise |
| Pr. 6 | In the same or congruent circles, congruent central angles have congruent arcs. | Proof - Not given |
| Pr. 7 | In the same or congruent circles, congruent arcs have congruent central angles. | Proof - Not given |
| Pr. 8 | In the same or congruent circles, congruent chords have congruent arcs. | Proof - Student Exercise |
| Pr. 9 | In the same or congruent circles, congruent arcs have congruent chords. | Proof - Student Exercise |
| Pr. 10 | A diameter perpendicular to a chord bisects the chord and its arcs. | Proof - Student Exercise |
| Pr. 11 | A perpendicular bisector of a chord passes through the center of the circle. | Proof - Not given |
| Pr. 12 | In the same or congruent circles, congruent chords are equally distant from the center. | Proof - Not given |
| Pr. 13 | In the same or congruent circles, chords that are equally distant from the center are congruent. | Proof - Not given |
p. 113 - Frame 3 - If a radius bisects a chord, then it is perpendicular to the chord.
p. 114 - Frame 4
| Pr. 1 | A tangent is perpendicular to the radius drawn to the point of contact. | Proof - Not given |
| Pr. 2 | A line is tangent to a circle if it is perpendicular to the outer end of a radius. | Proof - Not given |
| Pr. 3 | A line passes through the center of a circle if it is perpendicular to a tangent at its point of contact. | Proof - Not given |
| Pr. 4 | Tangents to a circle from an outside point are congruent. | Proof - Student Exercise |
| Pr. 5 | The line from the center of a circle to an outside point bisects the angle between the two tangents from the point to the circle. | Proof - Student Exercise |
p. 119 - Frame 6
| Pr. 1 | A central angle is measured by its intercepted arc. | Definition |
| Pr. 2 | An inscribed angle is measured by one-half of its intercepted arc. | Proof - Not given |
| Pr. 3 | In the same or congruent circles, congruent inscribed angles have congruent intercepted arcs. | Proof - Student Exercise |
| Pr. 4 | In the same or congruent circles, inscribed angles having congruent intercepted arcs are equal. | Proof - Student Exercise |
| Pr. 5 | Angles inscribed in the same or congruent arcs are congruent. | Proof - Student Exercise |
| Pr. 6 | An angle inscribed in a semicircle is a right angle. | Proof - Student Exercise |
| Pr. 7 | Opposite angles of an inscribed quadrilateral are supplementary. | Proof - Student Exercise |
| Pr. 8 | Parallel lines intercept congruent arcs on a circle. | Proof - Student Exercise |
| Pr. 9 | An angle formed by a tangent and a chord is measured by one-half of its intercepted arc. | Proof - Not given |
| Pr. 10 | An angle formed by two intersecting chords is measured by one-half the sum of the intercepted arcs. | Proof - Not given |
| Pr. 11 | An angle formed by two secants intersecting outside a circle is measured by one-half the difference of the intercepted arcs. | Proof - Not given |
| Pr. 12 | An angle formed by a tangent and a secant intersecting outside a circle is measured by one-half the difference of the intercepted arcs. | Proof - Not given |
| Pr. 13 | An angle formed by two tangents intersecting outside a circle is measured by one-half the difference of the intercepted arcs. | Proof - Not given |
p. 132 - Frame 15
| Pr. 1 | In any proportion, the product of the means equals the product of the extremes. | Proof - Not given |
| Pr. 2 | If the product of two numbers equals the product of two other numbers, either pair may be made the means of a proportion and the other pair may be made the extremes. | Proof - Not given |
| Pr. 3 | A proportion may be changed into a new (equal) proportion by inverting each ratio. | Proof - Not given |
| Pr. 4 | A proportion may be changed into a new proportion by interchanging the means or by interchanging the extremes. | Proof - Not given |
| Pr. 5 | A proportion my be changed into a new proportion by adding the terms of each ratio to obtain new first and third terms. | Proof - Not given |
| Pr. 6 | A proportion my be changed into a new proportion by subtracting the terms of each ratio to obtain new first and third terms. | Proof - Not given |
| Pr. 7 | If any three terms of one proportion equal the corresponding three terms of another proportion, the remaining terms are equal. | Proof - Not given |
| Pr. 8 | In a series of equal ratios, the sum of the numerators is to the sum of the denominators as any one number is to its denominator. | Proof - Not given |
p. 137 - Frames 21 to 23
| Pr. 1 | If a line is parallel to one side of a triangle, then it divides the other two sides proportionately. | Proof - Not given |
| Pr. 2 | If a line divides two sides of a triangle proportionately, it is parallel to the third side. | Proof - Not given |
| Pr. 3 | Three or more parallel lines divide any two transversals proportionately. | Proof - Not given |
| Pr. 4 | A bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides. | Proof - Not given |
p. 139 - Frames 24 to 27
| Pr. 1 | Corresponding angles of similar triangles are congruent. | Definition |
| Pr. 2 | Corresponding sides of similar triangles are proportional. | Definition |
| Pr. 3 | Two triangles are similar if two angles of one triangle are congruent respectively to two angles of the other. | AA Proof - Not given |
| Pr. 4 | Two triangles are similar if an angle of one triangle is congruent to an angle of the other and the sides including these angles are in proportion. | SAS similarity Proof - Not given |
| Pr. 5 | Two triangles are similar if their corresponding sides are in proportion. | SSS similarity Proof - Not given |
| Pr. 6 | Two right triangles are similar if an acute angle of one is congruent to an acute angle of the other. | Proof - Student Exercise |
p. 143 - Frames 29 & 30
| Pr. 1 | The altitude to the hypotenuse of a right triangle is the mean proportional between the segments of the hypotenuse. | Proof - In class |
| Pr. 2 | In a right triangle, either leg is the mean proportional between the hypotenuse and the projection of that leg on the hypotenuse. | Proof - Student exercise |
| Pythagorus | In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. | Proof - Not given |
p. 146 - Frames 34 & 35
| Pr. 1 | In a 30-60-90 right triangle, the leg opposite the 30° angle equals one-half the hypotenuse. | Proof - Student exercise |
| Pr. 2 | In a 30-60-90 right triangle, the leg opposite the 60° angle equals one-half the hypotenuse times the square root of 3. | Proof - Student exercise |
| Pr. 3 | In a 30-60-90 right triangle, the leg opposite the 60° angle equals the leg opposite the 30° angle times the square root of 3. | Proof - Student exercise |
| Pr. 4 | The altitude of an equilateral triangle equals one-half a side times the square root of 3. | Proof - Student exercise |
| Pr. 5 | In an isosceles right triangle, the leg opposite a 45° angle equals one-half the hypotenuse times the square root of 2. | Proof - Student exercise |
| Pr. 6 | In an isosceles right triangle, the hypotenuse equals a side times the square root of 2. | Proof - Student exercise |
| Pr. 7 | In a square, a diagonal equals a side times the square root of 2. | Proof - Student exercise |
| Geometry Summary - Part 1 | Geometry Summary - Part 3 | Back to Handouts |