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What are the congruent angles and why? Both of angles A are congruent to each other and both of angles C are congruent because the are alternate interior angles.

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Would side lengths of 3, 8, and 10 make a triangle? Yes
Would side lengths of 5, 7, and 11 make a triangle? No
Would side lengths of 6, 1, and 7 make a triangle? No

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If 2 sides of a triangle are 3 and 8 what are the possible lengths of the third side?
The third side must be greater than 7 but less than 11

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if a=b+c and c > 0, then a > b.

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A proof involving indirect reasoning

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All possibilities are considered and then all but one are proved false

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The lines that contain the altitudes of a triangle are concurrent at the orthocenter of the triangle. It can be inside, on, or outside the triangle

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Is the perpendicular segment from a vertex of the triangle to the line containing the opposite side

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The point of concurrency of the medians

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The center of the triangle that is inscribed in the triangle

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The point of concurrency of the angle bisectors of a triangle

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The circle is circumscribed about the triangle

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The point of concurrency of the perpendicular bisectors of a triangle

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The point at which the three lines intersect ta

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When three or more lines intersect at one point, they are concurrent.

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The length of the perpendicular segment from the point to the line

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A point is equidistant from two objects two objects if it is the same distance from the objects

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a segment connecting the midpoints of two sides of a triangle