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©1998 ThinkQuest
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©1998 ThinkQuest
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| Theorem 7.10 | A parallelogram with a diagonal that bisects opposite angles is a rhombus. |
| Theorem 7.11 | A quadrilateral with four congruent sides is a rhombus. |
| Theorem 7.12 | All altitudes of a trapezoid are congruent. |
| Theorem 7.13 | The median of a trapezoid is parallel to its bases. Its length is one-half the sum of the lengths of the two bases. |
| Theorem 7.14 | The base angles of an isosceles trapezoid are congruent. |
| Theorem 7.15 | If the base angles of a trapezoid are congruent, then the trapezoid is isosceles. |
| Theorem 7.16 | The diagonals of an isosceles trapezoid are congruent. |
| Theorem 7.17 | If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles. |
| Theorem 8.1 | In a proportion, the product of the extremes equals the product of the means. |
| Corollary | If the product of the extremes equals the product of the means, then a proportion exists. |
| Theorem 8.2 | If a/b = c/d, then: b/d = d/c; a/c = b/d; a+b/b = c+d/d; a-b/b = c-d/d; a/b = a+c/b+d. |
| Theorem 8.3 | Congruent triangles are similar. |
| Theorem 8.4 | Transitive Property of Triangle Similarity: If Triangle ABC – Triangle DEF and Triangle DEF – Triangle GHI, then Triangle ABC – Triangle GHI. |
| Postulate 18 | AA Similarity Postulate: If two angles of a triangle are congruent to two angles of another triangle, then the two triangles are similar. |
| Theorem 8.5 | Triangle Proportionality Theorem: If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the two sides proportionally. |
| Theorem 8.6 | If a line divides two sides of a triangle proportionally, then the line is parallel to the third side of the triangle. |
| Theorem 8.7 | SAS Similarity Theorem: If an angle of one triangle is congruent to an angle of another triangle and the corresponding sides that include these angles are proportional, then the triangles are similar. |
| Theorem 8.8 | SSS Similarity Theorem: If all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar. |
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Note: The concepts in this collection may
not be entirely accurate.
They are for reference only.
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