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| Question | Answer |
| Segment Addition Postulate | Two Lengths of a Segment add up to become a full length |
| Transitive Property of Equality | If a=b and b=c then a=c |
| Subtraction Property of Equality | Subtract expressions which are equal |
| Angle Addition Postulate | Add two angle measures to make one large angle measure |
| Substitution Property of Equality | If x=y, then x can be substituted in for y and vice versa |
| Pependicular Bisector Theorem |
If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Image:
Triangle 51 (image/jpeg)
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| Converse of the Perpendicular Bisector Theorem |
If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment
Image:
Triangle 52 (image/jpeg)
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| Angle Bisector Theorem |
If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.
Image:
Paste Image70 (image/gif)
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| Converse of the Angle Bisector Theorem | If a point is in the interior of an angle and is equidistant from the two sides of an angle, then it lies on the bisector of the angle |
| Circumcenter Theorem | The circumcenter (a.k.a a point equidistant from the vertices of a triangle where three perpendicular bisectors of the sides meet) of a triangle is equidistant from the verticies of the triangle |
| Incenter Theorem | The incenter (a.k.a a point equidistant from the sides of a triangle where three angle bisectors intersect) of a triangle is equidistant from the sides of the triangle. |
| Centroid Theorem |
The centroid (a.k.a a point two thirds the distance from each vertex to the midpoint of the opposite side) of a triangle is always two thirds the distance from a vertex to the midpoint of the opposite side.
Image:
Diagram11 (image/gif)
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| Triangle Midsegment Theorem | The segment connecting the midpoint of two sides of a triangle is parallel to the third side and is half as long to the third side. |
| Triangle Longer Side Theorem | If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle facing the shorter side |
| Triangle Larger Angle Theorem | If one angle of a triangle is larger than another angle, then the side opposite the larger angle will be longer than the side opposite the smaller angle |
| Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle must always be larger than the third side |
| Hinge Theorem |
If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is larger than the third side of the second
Image:
Hinge1 (image/jpeg)
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| Converse of the Hinge Theorem | |
| Base Angles Theorem |
In an isoceles triangle, the angles opposite the congruent sides are congruent
Image:
Base Angles (image/gif)
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| Polygon Exterior Angles Theorem |
The sum of the measures of the exterior angles of a convex polygon, at each vertex, is 360 degrees. To find each individual measure, divide 360 by n, n being the number of sides
Image:
Exterior Sum (image/gif)
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| Parallelogram Opposite Sides Theorem |
If a quadrilateral is a parallelogram, then the opposite sides are congruent
Image:
Ch8not5 (image/gif)
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| Parallelogram Opposite Angles Theorem |
If a quadrilateral is a parallelogram, then opposite angles are congruent
Image:
Parallelogram2 (image/png)
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| Parallelogram Consecutive Angles Theorem |
If a quadrilateral is a parallelogram, then the consecutive angles are supplementary
Image:
Ch8not8 (image/gif)
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| Parallelogram Diagonal Theorem | If a quadrilateral is a parallelogram, then its diagonals bisect each other |
| Parallogram Opposite Sides Parallel and Congruent Theorem |
If one pair of a quadrilateral's sides are congruent and parallel, then a quadrilateral is a parallelogram
Image:
Par Prop B4 (image/jpeg)
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| Parallelogram Diagonals Converse | If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram |
| Rhombus Corollary |
A quadrilateral is a rhombus if and only if it has four congruent sides
Image:
Slide 3 (image/jpeg)
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| Rectangle Corollary |
A quadrilateral is a rectangle if and only if it has four right angles
Image:
Slide 7 (image/jpeg)
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| Square Corollary |
A quadrilateral is a square if and only if it is a rhombus and a rectangle
Image:
Slide 10 (image/jpeg)
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| Rhombus Diagonals Theorem | A parallelogram is a rhombus if and only if its diagonals are perpendicular |
| Triangle Sum Theorem | The sum of the three interior angles of a triangle adds up to 180 degrees |
| Exterior Angle Theorem | The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles, and is equal to the sum of the other two interior angles |
| Polygon Interior Angles Theorem |
The sum of the interior angles of a polygon is equal to (n-2)*180, where n is the number of sides. To find each individual measure, divide (n-2)*180/n
Image:
Lesson3 Fig7 (image/gif)
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| Polygon Exterior Angles Theorem |
The sum of the measure of the exterior angles of a convex polygon, one angle at each vertex, is 180
Image:
Exterior Sum (image/gif)
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| Corollary to the Polygon Interior Angles Theorem | The sum of the measures of the interior angles of a quadrilateral is 360 degrees, a triangle is 180, a pentagon 720, etc |
| Parallelogram Opposite Sides Theorem |
If a quadrilateral is a parallelogram, then opposite sides are congruent
Image:
Ch8not5 (image/gif)
|
| Parallelogram Opposite Angles Theorem |
If a quadrilateral is a parallelogram, then opposite angles are congruent
Image:
Parallelogram2 (image/png)
|
| Parallelogram Consecutive Angles Theorem |
If a quadrilateral is a parallelogram, then consecutive angles are supplementary
Image:
Ch8not8 (image/gif)
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| Parallelogram Opposite Sides Parallel and Congruent Theorem |
If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram
Image:
Par Prop B4 (image/jpeg)
|
| Rhombus Corollary |
A quadrilateral is a rhombus if and only if it has four congruent sides
Image:
Slide 3 (image/jpeg)
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| Parallelogram Diagonals The0rem | A quadrilateral is a parallelogram if its diagonals bisect each other |
| Rectangle Corollary | A |
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