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A quad. with both pairs of opposite sides ǁ (Usually shown by a tilted rectangle.) Pg. 167 |
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Theorem 5-1 Opp. sides of a parallelogram |
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Opposite sides of a parallelogram are ≅ Pg. 167 |
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Theorem 5-2 Opp. <s of a parallelogram |
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Opposite <s of a parallelogram are ≅ Pg. 167 |
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Theorem 5-3 Diagonals of a parallelogram |
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Diagonals of a parallelogram bisect each other. Pg. 167 |
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Theorem 5-4 Starting with both pairs of opp. sides of a quad. ≅ |
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If both pairs of opposite sides of a quad. are ≅, then the quad. is a parallelogram Pg. 172 |
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Theorem 5-5 Starting with one pair of opp. sides of a quad. both ≅ and ǁ |
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If one pair of opp. sides of a quad. are both ≅ and ǁ, then the quad. is a parallelogram. Pg. 172 |
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Theorem 5-6 Starting with both pairs of opp. sides of a quad. ≅ |
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If both pairs of opp. <s of a quad. are ≅, then the quad. is a parallelogram. Pg. 172 |
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Theorem 5-7 Starting with diagonals of a quad bisect each other |
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If the diagonals of a quad. bisect each other, then the quad. is a parallelogram. Pg. 172 |
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Five Ways to Prove a Quad is a Parrallelogram |
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1. Show both pairs of opp. sides ǁ 2. Show both pairs of opp. sides ≅ 3. Show one pair opp. Sides ≅ and ǁ 4. Show both pairs opp. <s ≅ 5. Show diagonals bisect each other Pg. 172 |
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Theorem 5-8 Starting with ǁ lines |
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If two lines are ǁ, then all points on one line are equidistant from the other line. Pg. 177 |
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Theorem 5-9 ǁ lines and ≅ segments |
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If three ǁ lines cut off ≅ segments on one transversal, then they cut off ≅ segments on every transversal. Pg. 177 |
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Theorem 5-10 Midpoint of a side of a ∆ and ǁ lines |
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A line that contains the midpoint of one side of a ∆ and is ǁ to another side passes through the midpoint of the third side. Pg. 178 |
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Theorem 5-11 Joining midpoints of two sides of a ∆ |
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The segment that joins the midpoints of two sides of a ∆ 1. is ǁ to the third side 2. is half as long as the third side Pg. 178 |
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A quad. with four right <s
Pg. 184 |
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A quad. with four ≅ sides (Diamond)
Pg. 184 |
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A quad. with four right <s and four ≅ sides
*This could be called a rectangle or a rhombus Pg. 184 |
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Theorem 5-12 Diagonals of a Rectangle |
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The diagonals of a rectangle are ≅ Pg. 185 |
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Theorem 5-12 Diagonals of a rhombus |
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The diagonals of a rhombus are ┴ Pg. 185 |
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Theorem 5-14 Diagonals and <s of a rhombus |
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Each diagonal of a rhombus bisects two <s of the rhombus. Pg. 185 |
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Theorem 5-15 Midpoint of the hyp. of a right ∆ |
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The midpoint of the hyp. of a right ∆ is equidistant from the three vertices. Pg. 185 |
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Theorem 5-16 Parallelogram and rt. < |
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If an < of a parallelogram is a right <, then the parallelogram is a rectangle. Pg. 185 |
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Theorem 5-17 Consecutive sides ≅ |
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If two consecutive sides of a parallelogram are ≅, then the parallelogram is a rhombus. Pg. 185 |
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A quad. with exactly one pair of ǁ sides Pg. 190 |
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Base & Legs of a trapezoid |
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Bases- ǁ sides of the trapezoid
Legs- the other two sides Pg. 190 |
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A trapezoid with ≅ legs Pg. 190 |
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Theorem 5-18 Base <s of an isosceles trapezoid |
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Base <s of an isosceles trapezoid are ≅ Pg. 190 |
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The segment that joins the midpoints of the legs. |
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Theorem 5-19 Median of a trapezoid |
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The median of a trapezoid 1. is ǁ to the bases 2. has a length equal to the average of the base lengths Pg. 191 |
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