Set: Geometry
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All 39 Terms
| | Term | Definition |
|---|---|---|
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Reflexive Property | A quantity is congruent (equal) to itself. a = a |
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Addition Postulate | If equal quantities are added to equal quantities, the sums are equal. |
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Subtraction Postulate | If equal quantities are subtracted from equal quantities, the differences are equal. |
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Substitution Postulate | A quantity may be substituted for its equal in any expression. |
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Partition Postulate | The whole is equal to the sum of its parts. Also: Betweeness of Points: AB+BC=AC Angle Addition Postulate: m<ABC+m<CBD=m<ABD |
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Right Angles | All right angles are congruent. |
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Linear Pair | If two angles form a linear pair, they are supplementary. |
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Vertical Angles | Vertical angles are congruent. |
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Triangle Sum | The sum of the interior angles of a triangle is 180ยบ. |
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Base Angle Theorem | If two sides of a triangle are congruent, the angles opposite these sides are congruent. |
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Base Angle Converse | If two angles of a triangle are congruent, the sides opposite these angles are congruent. |
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Side-Side-Side (SSS) Congruence | If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. |
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Side-Angle-Side (SAS) Congruence | If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
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Angle-Side-Angle (ASA) Congruence | If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
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Angle-Angle-Side (AAS) Congruence | If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. |
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Hypotenuse-Leg (HL) Congruence (right triangle) | If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the two right triangles are congruent. |
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CPCTC | Corresponding parts of congruent triangles are congruent. |
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Angle-Angle (AA) Similarity | If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. |
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SSS for Similarity | If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. |
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SAS for Similarity | If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. |
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Side Proportionality | If two triangles are similar, the corresponding sides are in proportion. |
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Corresponding Angles | If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. |
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Alternate Interior Angles | If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. |
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Alternate Exterior Angles | If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. |
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Interiors on Same Side | If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. |
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Parallelograms about sides | * If a quadrilateral is a parallelogram, the opposite sides are parallel. *If a quadrilaterals is a parallelogram, the opposite sides are congruent |
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Parallelogram about angles | * If a quadrilateral is a parallelogram, the opposite angles are congruent. *If a quadrilateral is a parallelogram, the consecutive angles are supplementary. |
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Parallelogram about diagonals | * If a quadrilateral is a parallelogram, the diagonals bisect each other. *If a quadrilateral is a parallelogram, the diagonals form two congruent triangles. |
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Parallelogram | If one pair of sides of a quadrilateral is BOTH parallel and congruent, the quadrilateral is a parallelogram. |
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Rectangle | If a parallelogram has one right angle it is a rectangle. *A parallelogram has one right angle it is a rectangle. *A rectangle is a parallelogram with four right angles. |
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Rhombus | A rhombus is a parallelogram with four congruent sides. *If a parallelogram has two consecutive sides congruent, it is a rhombus. *A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. *A parallelogram is a rhombus if and only if the diagonals are perpendicular. |
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Square | A square is a parallelogram with four congruent sides and four right angles. *A quadrilateral is a square if and only if it is a rhombus and a rectangle. |
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Trapezoid | A trapezoid is a quadrilateral with exactly one pair of parallel sides. |
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Isosceles Trapezoid | An isosceles trapezoid is a trapezoid with congruent legs. *A trapezoid is isosceles if and only if the base angles are congruent. *A trapezoid is isosceles if and only if the diagonals are congruent. *If a trapezoid is isosceles, the opposite angles are supplementary. |
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Radius | In a circle, a radius perpendicular to a chord bisects the chord and the arc. *If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency. |
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Chords | In a circle, or congruent circles, congruent chords are equidistant from the center. (and converse). *In a circle, or congruent circles, congruent chords have congruent arcs. (and converse). *In a circle, parallel chords intercept congruent arcs. *In the same circle, or congruent circles, congruent central angles have congruent chords (and converse). |
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Tangents | Tangent segments to a circle from the same external point are congruent |
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Arcs | In the same circle, or congruent circles, congruent central angles have congruent arcs. (and converse) |
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Angles | An angle inscribed in a semi-circle is a right angle. *In a circle, inscribed circles that intercept the same arc are congruent. *The opposite angles in a cyclic quadrilateral are supplementary. *In a circle, or congruent circles, congruent central angles have congruent arcs. |
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- Radius → In a circle, a radius perpendicular to a chord bisects the chord and the arc. *If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency. - 1 miss