geometry Q: True of false?

Question

1. the incenter, centroid, and orthocenter are always inside the triangle. T or F?

2. It is not possible for a trapezoid to have 3 congruent sides. T or F?

Answer 1

1. F Look at an obtuse triangle, the orthocenter is outside
2. F as well

Answer 2

#2 is a difficult one because mathematicians have STILL not agreed on a definition of a trapezoid. Some textbooks define it as having EXACTLY one set of parallel lines, some define it as having AT LEAST one set of parallel lines. If you follow the latter definition, your answer would be false, because a square and a rhombus would both fit the definition of a trapezoid, and you can have 3 congruent sides. So it depends on what your textbook and teacher use as a working definition. Yeah, I know, it's ridiculous! It would be nice if the math world would come to a consensus. Hey, if nothing else, you've got a good basis to argue that question with your teacher....;)

Answer 3

1. False
2. False

Answer 4

God dammit, can no longer you only look on the photos interior the e book and parent it out your self? a million. Duh, that is real. it particularly is a theorem! 2. fake. they're perpendicular, yet they do no longer mandatory bisect one yet another. 3. real. The letters are no longer next to a minimum of one yet another, so that they are opposite angles. 4. fake. P and S are next to a minimum of one yet another (you may rewrite it as SPQR) 5. real. The letters are next to a minimum of one yet another. Lazy, cheating bastard. i will do those issues of my eyes closed.

Answer 5

Both of them are false.

Answer 6

1.true
2. true.