1. Katerina Palacios 10-1

2. The perpendicular bisector theorem states that if one point lies on the perpendicular bisector of a segment then it is equidistant from the two endpoints of the segment. The converse of the perpendicular bisector is that any point that is equidistant from the endpoints of a segment then lies on the perpendicular bisector of a segment A perpendicular bisector it is a line that bisects a segment

3. The angle bisector theorem states that if a a point lies in the bisector of an angle then this is equidistant from the other sides of the angle. A D C E AC=CD F D CK FD=DC J L M Q JL=LM The perpendicular bisector theorem states that if one point lies on the perpendicular bisector of a segment then it is equidistant from the two endpoints of the segment. B c D

4. The concurrency is when 3 or more lines intersect at one certain point in a triangle So the point of concurrency is the point where this lines are able to intersect. The circumcenter of the triangle is the name for this point of concurrency which can be located inside, outside or on the triangle but as long as there are 3 or more lines that are intersecting.

5. The incenter is the point that lies on the center of the inscribed circle that is located inside the triangle. incenter

6. A median of a triangle is a segment that the endpoints are the vertex of the triangle and also the midpoint that is located on the opposite side. While the centroid of the triangle is the point of the concurrecy of the medians tha are inside the the triangle. Everything is connected to eachother. median Centroid centroid

7. The altitude of a triangle is the sum of the two lengths of any sides must be greater than the remaining sides. The orthocenter of a triangle is the point of concurrency of the three altitudes that a triangle has. It can also be known as the intersection of the three altitudes that a triangle has. D E F

8. The exterior inequality is that the exterior angle must be supplementary to the adjacent angle so it is greater than either of the non adjacent interior angles.

9. The triangle inequality states that for any triangle the sum of the two side´s lengths has to be greater than the length of the side that is remaining. In other simple words you can pick up two sides measures and when you add those together then the sum will be greater than the measure of the third side. 3,4,6 3+4=7>6 2,3,4 2+3=5>4 5,6,10 5+6=11>10

10. To write an indirect proof : 1.First you have to identify the conjecture or what you want to prove. 2.Then you should assume the opposite of the conclusion you want. 3.Then use what is called direct reasoning to lead to the contradiction 4.Then conclude by saying that the conjecture was correct. Given: JKL is right angle Prove: JKL does not have an obtuse angle JKL has an obtuse angle. <K is obtuse M<K +m<L =90 M<K =90 –mL M 90 90-m 90 M<L<0 JKL does not have an obtuse angle

11. Given : m m<R Prove: QR>QP QR=QP QR<QP then m<P =m<R QR does not =QP Isosceles Theorem QR>QP, so the statement we tried to prove was false

12. The hinge theorem states that if the sides of two triangles are congruent than the first angle has to be larger than the second one. So the converse of the hinge theorem is that if two sides of a triangle are congruent to the sides of another than the third side of the first triangle is congruent to the third side of the other. 4 8 4 9585 44 7 66 7 67 6 6 9 70 5 5 6 5 5 9 11 0 105