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Vocab in Relationships in Triangles

What is inverse? negate both the hypothesis (if part) and the conclusion (then part)
What is converse? switch the hypothesis and conclusion
What is the contrapositive? negate and switch, inverse and converse the original conditional
What is a midsegment? A segment connecting the midpoints of two sides in a triangle
What are the properties of a midsegment? The midsegment is parallel to the side not including the midpoints and the midsegment is half the length of the the parallel side
What formulas justify the midsegment properties? slopes that are the same prove parallel and distances would show the half/doubling relationship between the segments
What is a median in a triangle? A segment drawn from an angle to the opposite side to its midpoint, therefore dividing the side into 2 congruent parts
What is an altitude in a triangle? A segment drawn from an angle to the opposite side forming a right angle
What is an angle bisector? A segment that divides an angle into two congruent angles
How can three lengths form a triangle? The two smallest lengths must sum to be more than the longest length
If given 2 lengths, how do you find the possibilities for the third side? You can guess and check till you're blue...or to find the smallest range subtract the given lengths and to find the largest range, add the two given lengths, use the less than inequalities to show the range
If you have sides of 20 and 50, what is an inequality to represent the possibilities of the third side? 30 < 3rd side < 70
What are the relationships between sides and angles in a triangle? the smallest side is opposite the smallest angle and the largest angle is opposite the largest side
What is inductive reasoning? First negate the assumption, then show that negated assumption leads to a contradiction, then conclude the assumption must have been false making the original hypothesis true
Why does inductive reasoning use the contrapositive? They are the same process of negating and switching and coming back to the original hypothesis must have been true
What are the points of concurrency? centroid, circumcenter, incenter, orthocenter
How can you remember the points of concurrency? Peanut Butter Cookies Are Best In Milk Chocolate And Ovaltine
How do you construct a circumcenter? Intersection of 3 perpendicular bisectors, should see two little arcs above the line and two little arcs below the line, the perpendicular bisector is the line connecting those arc intersections,use the endpoints of the sides of the triangle.
What is the circumcenter of a triangle? The center of a circumscribed circle around the triangle
How do you construct an incenter? Intersection of 3 angle bisectors, should see 1 big arc and two little arcs at each angle, draw the angle bisector from the angle to the little arc intersection.
How do you construct a centroid? Intersection of 3 medians, must find midpoints of the sides like circumcenter construction, BUT the median is drawn from the angle to the midpoint so there will not be a right angle.
How do you construct an orthocenter? Intersection of 3 altitudes
What is the significance of the centroid in terms of the length of the median? The centroid divides the median into a 2/3 and 1/3 ratios. The 2/3 part of the median is from the angle to the centroid and the 1/3 part of the median is from the centroid to the side(midpoint)
What was the title of the unit #5? Relationships in Triangles