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39 Cards in this Set
- Front
- Back
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What is the formula used to find the sum of the angle measures in a polygon? |
(n-2) * 180 *=multiply |
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Polygon Interior Angles Theorem |
The sum of the measures of the interior angles of a convex n-gon is (n-2)180 |
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Corollary to Polygon Interior Angles Theorem: Interior Angles of a Quadrilateral |
The sum of the measures of the interior angles of a quadrilateral is 360 degrees. |
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Polygon Exterior Angles Theorem |
The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360 degrees. *note: This is true no matter how many sides the convex polygon has. |
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Parallelogram |
Quadrilateral with both pairs of opposite sides parallel. |
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If a quadrilateral is a parallelogram, then its opposite sides are __________ |
_________ congruent. *sides |
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If a quadrilateral is a parallelogram, then its opposite angles are __________
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_________ congruent. *angles |
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If a quadrilateral is a parallelogram, then its consecutive angles are __________ |
__________ supplementary. |
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If a quadrilateral is a parallelogram, then its diagonals _______ each other. |
_____ bisect ______ |
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Five ways to prove that a quadrilateral is a parallelogram: |
1: Show both pairs of opposite sides are parallel. 2: Show both pairs of opposite sides are congruent. 3: Show both pairs of opposite angles are congruent. 4: Show one pair of opposite sides is both parallel and congruent. 5: Show diagonals bisect each other. |
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What do you use if you want to show that both pairs of opposite sides are congruent when proving a quadrilateral is a parallelogram? |
The distance formula four times. |
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What is the distance formula? |
D=the square root of (X2-X1)^2+(Y2-Y1)^2 (the square root of x two minus x one quantity squared, plus the y two minus y 1 quantity squared). *Be sure to show EVERY LINE OF WORK, or she will take off points :) |
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What do you use if you want to show that both pairs of opposite sides are parallel when proving a quadrilateral is a parallelogram? |
Slope formula four times. |
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What is the slope formula? |
m=y2-y1 -------- x2-x1 (m equals y two minus y one over/divided by x two minus x one) *m is the label we use for slope, and x and y refer to the coordinates given in the problem. |
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What do you use if you want to show that one pair of opposite sides are both parallel and congruent when proving a quadrilateral is a parallelogram? |
The distance formula twice and the slope formula twice. |
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What do you use if you want to show that the diagonals bisect each other when proving a quadrilateral is a parallelogram? |
The midpoint formula twice |
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What is the midpoint formula? |
midpt=(x1+x2 y1+y2) ( ---------- ---------) ( 2 , 2) (Midpoint equals x one plus x two over/divided by two, and y one plus y two over/divided by two) *The answer is taken as an ordered pair, looking like this: (x , y) |
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Rectangle |
Parallelogram with four right angles (meaning four congruent angles) |
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Rhombus |
Parallelogram with four congruent sides. |
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Square |
Parallelogram with four right angles (meaning the angles are congruent), and four congruent sides. *Has any properties that a rhombus and/or rectangle have |
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A parallelogram is a rhombus IFF its diagonals are _________. |
______ perpendicular |
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A parallelogram is a rhombus IFF each diagonal ______ a pair of opposite angles. |
_____ bisects _____ |
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A parallelogram is a rectangle IFF its diagonals are _______ |
_______ congruent |
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Trapezoid |
A quadrilateral with exactly one pair of parallel sides (called bases). |
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Is a trapezoid a parallelogram? |
NO!!!! |
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Does a trapezoid follow the rules of a parallelogram? |
NO! Because it is NOT A PARALLELOGRAM. :) |
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The "upper" base angles and the "lower" base angles are _____. |
Congruent. *See 8.5 notes for clarification* |
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Isosceles Trapezoid |
A trapezoid with congruent legs. |
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When referring to a trapezoid, what are the legs? |
The sides of the trapezoid that aren't parallel. |
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If a trapezoid is isosceles, then each pair of base angles is ________. |
________ congruent. |
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If a trapezoid has a pair of congruent _____ _______, then it is an isosceles trapezoid. |
_____ base angles _____ |
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A trapezoid is isosceles IFF its diagonals are _______. |
________ congruent. |
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Midsegment of a Trapezoid |
A segment that connects the midpoints of its legs. |
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Midsegment Theorem for Trapezoids |
The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. |
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What is the midsegment formula for trapezoids? |
midsegment=AB+CD ---------- 2 (AB plus CD over/divided by two)
*BE CAREFUL: When putting this in a calculator, be sure to either put parenthesis around the top of the equation, or type them in separately. -Example: 2+4=6 divided by 2=3 - Example: (2+4) -------- 2 - Either of these ways is correct :) |
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What are the characteristics of a parallelogram? |
1. Consecutive angles are supplementary 2. Both pairs of opposite sides are congruent 3. Diagonals bisect each other 4. Both pairs of opposite angles are congruent 5. Both pairs of opposite sides are parallel |
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What are the characteristics of a rhombus? |
1. Consecutive angles are supplementary 2. Diagonals bisect opposite angles 3. Both pairs of opposite sides are congruent 4. Diagonals are perpendicular 5. Diagonals bisect each other 6. Equilateral 7. Both pairs of opposite angles are congruent 8. Both pairs of opposite sides are parallel. |
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What are the characteristics of a rectangle? |
1. Consecutive angles are supplementary 2. Equiangular 3. Both pairs of opposite sides are congruent 4. All angles are right angles 5. Diagonals bisect each other 6. Both pairs of opposite sides are parallel 7. Diagonals are congruent 8. Both pairs of opposite angles are congruent |
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What are the characteristics of a square? |
1. Consecutive angles are supplementary 2. Diagonals bisect opposite angles 3. Equiangular 4. Both pairs of opposite sides are congruent 5. Diagonals are perpendicular 6. All angles are right angles 7. Diagonals bisect each other 8. Equilateral 9. Both pairs of opposite angles are congruent 10. Both pairs of opposite sides are parallel 11. Regular 12. Diagonals are congruent |
