Term
Side-Side-Side Postulate
(SSS) |
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Definition
| If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent |
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Term
Side-Angle-Side Postulate
(SAS) |
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Definition
| If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two angles are congruent |
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Term
Angle-Side-Angle Postulate
(ASA) |
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Definition
| If two angles and the included side of one triangle are congruent to two angles and the included side of another tirangle, the the two angles are congruent |
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Term
Angle-Angle-Side Theorem
(AAS) |
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Definition
| If 2 angles and a nonincluded side of one triangle are congruent to two angels and the corresponoding nonincluded side of another triangle, then the triangles are congruent |
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Term
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Definition
- The congruent sides of isosceles triangles are called the legs
- The third side is the base
- The two congruent sides form the vertex angle
- The other two angles are the base angles
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Term
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then |
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Definition
| then the angles opposite those sides are congruent |
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Term
Corollary for Triangles
An equilateral triangle is also |
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Definition
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Term
Corollary for Triangles
An equilateral triangle has |
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Definition
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Term
Corollary for Triangles
The bisector of the vertex angle of an isosceles triangle is |
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Definition
| is perpendicular to the base at its midpoint |
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Term
Converse of The Isosceles Triangle Theorem
If two angles of a triangle are congruent, then |
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Definition
| then the sides opposite the angles are congruent |
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Term
Corollary for Triangles
If a triangle is equiangular, then the triangle is |
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Definition
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Term
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Definition
- The side opposite the right angle is the longest side and is called the hypotenuse
- The other two sides are called legs
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Term
Hypotenuse-Leg (HL) Theorem
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Definition
| If the hypotenuse and a leg of one right traingle are congruent to the hypotenuse and leg of another right triangle, then the tirangles are congruent |
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Term
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Definition
| A median of a triangle is a segment from a vertex to the midpoint of the opposite side |
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Term
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Definition
| the perpendicular segment from a vertex to the line containing the opposite side |
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Term
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Definition
a line (or ray or segment) that is perpendicular to the segment at it's midpoint
*in a plane, a segment has exactly one perpendicular bisector |
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Term
Theorem
If a point lies on the perpendicular bisector of a segment, then |
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Definition
Theorem
then the point is equidistant from the endpoints of the segment |
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Term
Theorem
If a point is equidistant from the endpoints of a segment, then |
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Definition
Theorem
then the point lies on the perpendicular bisector of the segment |
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Term
Theorem
If a point lies on the bisector of an angle, then |
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Definition
Theorem
then the point is equidistant from the sides of the angle
(the distance from a point to a line is defined as the length of the perpendicualr segment from the point to the line) |
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Term
Theorem
If a point is equidistant from the sides of an angle, then |
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Definition
Theorem
then it lies on the bisector of the angle |
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