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Definition
| Is a perpendicular segment from a vertex to the side opposite. |
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Definition
| Is a segment or ray that divides a vertex of the triangle into two smaller, equal angles. |
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Definition
| The common point of intersection of the three medians of a triangle. |
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Definition
| Is the point where the perpendicular bisectors meet. |
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Definition
| When three or more lines or segments meet at a common point |
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Definition
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Definition
| In a right triangle, the side opposite the right angle |
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Definition
| The point where the angle bisectors meet |
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Definition
| In a right triangle, the two sides that form the right angle. |
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Definition
| A segment that joins a vertex of the triangle and the midpoint of the side opposite that vertex |
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Definition
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Term
orthocenter
OR-tho-SEN-tur |
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Definition
| The point where the altitudes meet. |
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Definition
| A segment or line that contains the midpoint of a side of a triangle and is perpendicular to that side. |
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Pythagorean Theorem
puh-THA-guh-REE-uhn |
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Definition
| In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse |
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Term
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Definition
| The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint. |
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Theorem 6-2
Isosceles Triangle Theorem |
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Definition
| If two sides of a triangle are congruent, then the angles opposite those sides are congruent. |
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Term
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Definition
| The median from the vertex angle of an isosceles triangle lies on the perpendicular bisector of the base and the angle bisector of the vertex angle. |
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Theorem 6-4
Converse of Isosceles Triangle Theorem |
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Definition
| If two angles of a triangle are congruent, then the sides opposite those angles are congruent. |
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Term
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Definition
| A triangle is equilateral if and only if it is equiangular. |
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Definition
| If two legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. |
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Term
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Definition
| If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding angle of another right triangle, then the triangles are congruent. |
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Term
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Definition
| If one leg and an acute angle of one right triangle are congruent to the corresponding leg and angle of another right triangle, then the triangles are congruent. |
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Term
Theorem 6-9
Pythagorean Theorem |
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Definition
| In a right triangle, the square of the length of the hypotenuse c is equal to the sum of the squares of the lengths of the legs a and b. |
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Term
Theorem 6-10
Converse of Pythagorean Theorem |
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Definition
| If c is the measure of the longest side of a triangle, a and b are the lengths of the other two sides, and c2 = a2 + b2, then the triangle is a right triangle. |
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Term
Theorem 6-11
Distance Formula |
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Definition
If d is the measure of the distance between two points with coordinates (x1, y1) and (x2,y2), then
d = \/(X2 -X1)2 +(y2+Y1)2. |
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Term
Postulate 6-1
HL Postulate |
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Definition
| If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. |
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