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Points that are in a line |
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Is a flat surface or a 2-dimensional object, stretching to infinity in all directions. |
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Points that are on the same plane |
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How many points do you need to make a point? |
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To make a plane, you need.... |
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You need three non-collinear points to make a plane. |
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If two lines intersect, then they intersect in _ points |
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If two planes intersect, then they intersect in _ points |
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Always two endpoints. Has infinite number of points in between ends of this. |
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One endpoint forever in one direction, the other doesn't go on. |
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Two collinear rays with the same endpoint. |
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Lines that do not lie in the same plane (non-coplanar) that never intersect. |
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A ____ is formed by two rays and a endpoint. Rays are sides of _____. The end is the vertex of the ______. |
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Angle that is less than 90 degrees |
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Angle that is exactly 90 degrees |
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More than 90 degrees, but less than 180 degrees. |
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Two angles whose sides are opposite rays. |
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Adjacent angles are angles just next to each other. Adjacent angles share a common vertex and a common side, but do not overlap. |
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Two angles whose measures have a sum of 90 degrees. |
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Two angles that add up to 180 altogether. |
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Same position on each line. |
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-If a transversal intersects two // lines⇒corresponding angles are ≅ -If a transversal intersects two // lines⇒alternate interior angles are ≅ -If a transversal intersects two // lines⇒alternate interior angles are ≅ -If a transversal intersects two // lines⇒alternate exterior angles are ≅ - If a transversal intersects two // lines⇒same side interior angles are supplementary. -If a transversal intersects two // lines⇒same side exterior angles are supplementary. |
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Have congruent corresponding parts and all angles and sides are congruent. |
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Shapes are congruent from before to after. No changes. |
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Know two angles, and you can assume that the third angle is congruent. |
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Corresponding Parts of Congruent Triangles are Congruent. |
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Isosceles Triangle Theorem |
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If two sides of a triangle are congruent, then the angles opposite of those are congruent. |
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If 2 angles of a triangle are congruent, then the sides opposite are are congruent |
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In a right triangle, if you have a hypotenuse and legs are congruent. |
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At least two sides congruent. |
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When three or more lines intersect |
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The point where the three lines intersect. |
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Starts at vertex and ends at midpoint of opposite sides. 3 ____ in a triangle. |
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Starts at vertex and hits opposite sides at right angles. ______ can be outside of triangle. |
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Starts at vertex and _____ vertex angle. |
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Does not have to start at vertex. Starts at midpoint of base and makes right angles. |
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Point of concurrency for median isosceles triangles. |
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All alternate lines meet up at middle of isosceles triangle. For altitudes. |
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Perpendicular bisector point of concurrency. |
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Angle bisector point of concurrency. |
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Is a quadrilateral with both pairs of opposite sides parallel. |
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Is a parallelogram with 4 congruent sides. |
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Is a parallelogram with 4 right angles. |
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Is a parallelogram with 4 congruent sides and right angles. |
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Is a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent. |
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Is a quadrilateral with exactly one pair of parallel sides. |
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Is a ____ whose non-parallel sides are congruent. |
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Properties of Parallelograms |
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-Opposite sides are congruent. - Opposite angles are congruent. - Consecutive angles are supplementary. - One pair of opposite sides are both parallel and congruent. - Diagonals bisect each other. |
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-All sides congruent. -Each diagonal bisects opposite angles. -Diagonals are perpendicular |
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-Opposite sides are congruent. -Opposite angles are congruent. -Same sides angles are supplementary. -Diagonals bisect each other. -4 right angles -Diagonals are congruent. |
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-All sides congruent. -Each diagonal bisects opposite angles. -Diagonals are perpendicular -Opposite sides are congruent. -Opposite angles are congruent. -Same side angles are supplementary. -Diagonals bisect eachother. -4 right angles -Diagonals are congruent. -Opposite sides are congruent. -Opposite angles are supplementary. -Consecutive angles are supplementary. -Diagonals bisect each other. -One pair of opposite sides are both parallel and congruent. |
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Only one pair of opposite sides are parallel (bases). 2 angles that share a leg are supplementary. |
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Isosceles Trapezoid Properties |
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Legs are congruent. Base angles are congruent. Diagonals are congruent. |
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-Two pairs of consecutive sides are congruent. -No pairs of opposite sides are congruent. -Diagonals are perpendicular. -One diagonal bisects opposite angles. -One diagonal divides into two congruent triangles. -Other diagonal divides into two isosceles triangles. |
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Polygons are similar if... |
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If corresponding angles and sides are proportional |
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