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10 Cards in this Set
- Front
- Back
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Angle-Angle Similarity (AA~) Postulate (Postulate 7-1)
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If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
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Side-Angle-Side Similarity (SAS~) Theorem (Theorem 7-1)
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If an angle of one triangle is congruent to an angle of second triangle and the sides that include the two angles are proportional, then the triangles are similar.
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Side-Side-Side Similarity (SSS~) Theorem (Theorem 7-2)
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If the corresponding sides of two triangles are proportional, then the triangles are similar.
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Theorem 7-3
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are what to the original triangle and to each other? |
similar
The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. |
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Corollary 1 to Theorem 7-3
The length of the altitude to the hypotenuse of a right triangle is the geometric mean of what? |
the lengths of the segments of the hypotenuse
The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. |
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Corollary 2 to Theorem 7-3
The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the lengths of what? |
the hypotenuse and the length of the segment of the hypotenuse adjacent to the leg.
The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to the leg. |
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Side-Splitter Theorem (Theorem 7-4)
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If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
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Corollary to the Side Splitter Theorem
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If three parallel lines intersect two transversals, then the segments intercepted on the transversal are proportionate.
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Triangle-Angle-Bisector Theorem (Theorem 7-5)
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If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
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