Chapter 5 Review Circles

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A median of a triangle is a segment from a vertex to the midpoint of the opposite side

always

A midsegment is parallel to the triangle's third side

always

A point is equidistant from two figures if the point is the same distance from each figure

always

A segment that connects the midpoints of two sides of a triangle is a midsegment

always

If a point is on the bisector of an angle, then it is equidistant from he two sides of the angle

always

In a plane, if a point is on the perpendicular bisector of a segment, then it equidistant from the endpoints of the segment

always

In a triangle, the shortest side lies opposite the smallest angle

always

Indirect proofs begin with negating the conclusion

always

It is possible to construct a triangle with side lengths a, a, and a

always

It is possible to construct a triangle with side lengths of 4, 4, and 6

always

The centroid falls inside the triangle

always

The incenter falls inside the triangle

always

The point of concurrency of the three medians of a triangle is called the centroid

always

The sum of the lengths of any two sides of a triangle is greater than the length of the third side

always

When 3 or more lines, rays, or segments intersect at the same point , they are called concurrent

always

A midsegment is congruent to the triangle's third side

never

A midsegment is perpendicular to the triangle's third side

never

A midsegment is twice as long as the triangle's third side

never

An incenter is the point of concurrency of the three perpendicular bisectors of a triangle

never

Concurrent lines are parallel

never

If a point is on the bisector of an angle, then it is twice the distance from one side than it is from the other

never

If two sides of a triangle are 4 and 14, the third side can lie between 10 and 18 inclusive

never

Indirect proofs begin with negating the hypothesis

never

It is possible to construct a triangle with side lengths 4, 4, and 9

never

It is possible to construct a triangle with side lengths of 2, 2, and 4

never

The centroid falls outside the triangle

never

The hypotenuse is the shortest side of a right triangle

never

The incenter falls outside the triangle

never

The incenter lies on one of the three sides a triangle

never

The leg is the longest side of a right triangle

never

The orthocenter falls inside the triangle

never

It is possible to construct a triangle with side lengths a, a, and a+b

sometimes

The circumcenter falls inside the triangle

sometimes

The circumcenter falls outside the triangle

sometimes

The circumcenter is the point of concurrency of the three perpendicular bisectors of a triangle

sometimes

The orthocenter falls outside the triangle

sometimes


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