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| 69650544 | AA Similarity Postulate | If two angles of one triangle are cnogruent to two angels of another triangle, then the triangles are similar. | |
| 69650545 | SAS Similarity Theorem | If an angel of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar. | |
| 69650546 | SSS Similarity Theorem | If the sides of two triangles are in proportion, then the triangles are similar. | |
| 69650547 | Corollary (Theorem 7-3) | If three parallel lines intersect two transversals, then they divide the transversals proportionally. | |
| 69650548 | Triangle Angle- Bisector Theorem | If a ray bisects an angel of a triangle, then it divides the opposite side into segments proportional to the other two sides. | |
| 69650549 | Theorem 8-1 | If the altitudes is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. | |
| 69650550 | Corollary 1 & Corollary 2 (to Theorem 8-1) | 1. When the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometetic mean between the segments of the hypotenuse. 2. When the altitude is drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg. | |
| 69650551 | Pythagorean Theorem | In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. | |
| 69650552 | Theorem 8-3 | If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangles is a right triangle.
---- If c2=a2+b2, then M| | |
| 69650553 | Theorem 8-4** | If c²| | |
| 69650554 | Theorem 8-5** | If c²>a²+b², then m∠C >90, and ΔABC is obtuse. | |
| 69650555 | 45'-45'-90' Theorem | In a 45°-45°-90° Triangle, the hypotenuse is √2 times as long as a leg. | |
| 69650556 | 30'-60'-90' Theorem | In a 30°-60°-90° Triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg. | |
| 69650557 | Theorem 9-1 | If a line is tangent to circle, then the line is perpendicular to the radius drawn to the point of tangency. | |
| 69650558 | Corollary (Theorem 9-1) | Tangets to a circle from a point are congruent | |
| 69650559 | Theorem 9-2 | If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. | |
| 69650560 | Arc Addition Postulate | The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs. | |
| 70195365 | Theorem 9-3 | In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent. | |
| 70195366 | Theorem 9-4 | In the same circle or in congruent circles: (1) Congruent arcs have congruent chords (2) Congruent chrods have congruent arcs. | |
| 70195367 | Theorem 9-5 | A diameter that is perpendicular to a chord biscets the chord and its arc. | |
| 70195368 | Theorem 9-6 | In the same circle or in congruent circles: (1) Chrods equally distant from the center(or centers) are congruent. (2) Congruent chords are equally distant from the center(or centers) | |
| 70195369 | Theorem 9-7 | The measure of an inscribed angle is equal to half the measure of its intercepted arc. | |
| 70195370 | Theorem 9-7 Corollary | 1. If two inscribed angles intercept the same arc, then the angles are congruent. 2. An angle inscribed in a semicircle is a right angle. 3. If a quadrilateral is inscribed in a circle, them its opposite angles are supplementary | |
| 70195371 | Theorem 9-8 | The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc | |
| 70195372 | Theorem 9-9 | The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measure of the intercepted arcs. | |
| 70195373 | Theorem 9-10 | The measure of an angle formed by two secants, two tangents, or a secant a tangent drawn from a point outside a circle is equal to half the diffrence of the measures of the intercepted arcs. | |
| 70195374 | Theorem 9-11 | when two chords interscet inside a circle, the product of the segments of one chord equals the product of the segments of the other chord. | |
| 70195375 | Theorem 9-12 | when two secants segments are drawn to a circle from an external point the product of one secant segments and its external segments equals the product of the other secant segment and its extreanl segments. | |
| 70195376 | Theorem 9-13 | when a secant and a tangent segment are drawn to a circle from an external to the square of the tangent segment. | |
| 70195377 | Construction 1 | Given a segment construct a segment congruent to the given segment. | |
| 70195378 | Construction 2 | Given an angle construct an angle congruent to the given angle. | |
| 70195379 | Construction 3 | Given an angle, construct the bisector of the angle | |
| 70195380 | Construction 4 | Given a segment constuct the perpendicular bisector of the segment. | |
| 70195381 | Construction 5 | Given a point on a line, construct the perpendicular to the line at the given point. | |
| 70195382 | Construction 6 | Given the point outside a line, construct the perpendicular to the line from the given point | |
| 70195383 | Construction 7 | Given a point outside the line construct the parallel to the given line through the given point | |
| 70195384 | Theorem 10-1 | The bisector of the angles of a triangle intersect in a point that is equidisant from the three sides of the triangle | |
| 70195385 | Theorem 10-2 | The perpendicular bisector of the sides of a triangle intersect in a point that is equidisant from the three vertices of the triangle | |
| 70195386 | Theorem 10-3 | The lines that contian the altitudes of a triangle intersect in a point. | |
| 70195387 | Theorem 10-4 | The medians of a triangle intersect in a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. | |
| 70195388 | Construction 8 | Given a point on a circle construct the tangent to the circle at the given point | |
| 70195389 | Construction 9 | Given a point outside a circle construct a tangent to the circle form the given point | |
| 70195390 | Construction 10 | Given a triangle, circumscribe a circle about the triangle | |
| 70195391 | Construction 11 | Given a triangle inscirbe a circle in the triangle | |
| 70195392 | Construction 12 | Given a segment divide the segment into a given number of congruent parts. | |
| 70195393 | Construction 13 | Given three segments, construct a fourth segment, so that the four segments are in proportion. | |
| 70195394 | Construction 14 | Given two segments construct their geometric mean. | |
| 70195395 | Postulate 17 | The area of a square is the square of the lenght of a side, (A=s²) | |
| 70195396 | Area Congruence Postulate | if 2 figures are congruent, then they have the same area | |
| 70195397 | Area Addition Postulate | The area of a region is the sum of the areas of its nonoverlapping parts. | |
| 70195398 | Theorem 11-1 | The area of a rectangle equals teh product of its base and height.(A=bh) | |
| 70195399 | Theorem 11-2 | The area of a parallelogram equals the product of a base and the height to the base(A=bh) | |
| 70195400 | Theorem 11-3 | The area of a triangle equals half the product of a base and the height to that base (A=½bh) | |
| 70195401 | Theorem 11-4 | The area of a rhombus equals half the product of its diagonals(A=½d1d2) | |
| 70195402 | Theorem 11-5 | The area of the trapezoid equals half the product of the height and the sum of the base (A=½h(b1+b2) | |
| 70195403 | Theorem 11-6 | the area of a regular polygon is equal to half the product of the apothem and the perimeter.(A=½ap) |
