Name. 1) If Q is the vertex angle of isosceles PQR, and RA is a median, find m QR Q. 4 inches A. 2) Which side is the dot closest to?

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1 enters of Triangles acket 1 Name 1) If Q is the vertex angle of isosceles QR, and R is a median, find m QR Q 4 inches R 2) Which side is the dot closest to? an you draw a point that is the same distance away from the 3 sides? This point is called the incenter. dd markings to indicate that point is the triangle s incenter. ut Why is it called the INcenter???

2 enters of Triangles acket 2 3) Sketch the incenter of each triangle and show markings in two different ways that indicate it is the incenter. 4) In the triangle below, point is the incenter. Find the measures of angles x, y, and z. x y 24 o z 30 o 5) In the triangle below, point Q is the incenter. Find the measures of angles w, x, y, and z. w x Q z 18 o 34 o y

3 enters of Triangles acket 3 6) In the triangle below, point is the incenter. Find the measures of angles x, y, and z. x y 22 o z 26 o 7) In the triangle below, point Q is the incenter. Find the measures of angles w, x, y, and z. x 23 o Q z 21 o w y y z 8) In isosceles,. If is the triangle s incenter, find the measures of angles w, x, y, and z. 34 o w x

4 enters of Triangles acket 4 9) Which vertex is the dot closest to? 10) an you draw a point that is the same distance away from the 3 vertices? This point is called the circumcenter. 11) What can you add to your diagram to show that you drew the circumcenter? dd markings to indicate that point is the triangle s circumcenter. ut Why is it called the IRUMcenter???

5 enters of Triangles acket 5 12) In each triangle below, add markings to show that the given point is the circumcenter, and construct the circumscribed circle. 13) If is the circumcenter of the triangle below, which of the following choices must be correct? (ircle all that apply) ] ] ] D] E] is isosceles. F] If, then G]

6 enters of Triangles acket 6 14) If Q is the circumcenter of the triangle below, which of the following choices must be correct? (ircle all that apply) ] D ] ] Q D] E] is isosceles. F] 15) hoose incenter or circumcenter for each of the following: a] If is the center of the triangle s inscribed circle, then point is the (incenter/circumcenter) D E b] If is the center of the triangle s circumscribed circle, the n point is the (incenter/circumcenter) c] If the 3 sides of the triangle are bisected, point is the (incenter/circumcenter) d] If the 3 angles of the triangle are bisected, then point is the (incenter/circumcenter) F e] If, then point is the (incenter/circumcenter) f] If, then point is the (incenter/circumcenter)

7 enters of Triangles acket 7 16) Determine whether each point shows the triangle s incenter, or circumcenter. a] b] c] d] e] f] 25 o 25 o D E 30 o 30 o 35 o 35 o 17) The centroid of a triangle is the point where the 3 medians intersect. 18) a] The incenter of a triangle is the point where the 3 intersect. It is equidistant from the triangle s 3. It is the center of the triangle s. b] The circumcenter of a triangle is the point where the 3 intersect. It is equidistant from the triangle s 3. It is the center of the triangle s.

8 enters of Triangles acket 8 c] The centroid of a triangle is the point where the 3 intersect. 19) The centroid has a special feature an you figure it out? 20) 21)

9 enters of Triangles acket 9 22) In, m F 9, and m GE Find m G and m E. E G F D 23) In the diagram, m MS 2x 17, m NS 4x 26, and m S 27. N a] Find x. a] Find S S b] Find M c] Find NS M Q L d] Find SQ 24) In LMN, m RL 21, and m SQ 4. Find m LS and m NQ N R S M Q L

10 enters of Triangles acket10 25) In GHJ, m 2. 9, and m H H a] Find b] Find H c] Find J d] Find J G J 26) In LMN, m S 7, and m NQ Find m M and m NS N R S M Q L 27) In the diagram, m D 10, and m G a] Find GD b] Find G c] Find FG d] Find F

11 enters of Triangles acket11 28) owser: The centroid is the point where the triangle s 3 medians intersect. Mario: The centroid divides each median into a ratio of 1:2 Luigi: The centroid is located 2/3 of the way from each vertex to its opposite side. Who is correct? 29) Determine whether each picture shows the triangle s incenter, circumcenter, or centroid. a] b] c] d] e] f] 25 o 25 o 30 o 30 o E 35 o 35 o

12 enters of Triangles acket12 30) The orthocenter is the point where the triangle s three intersect. 31) Name the 3 properties of the incenter, and provide diagrams to help you study. a] b] c]

13 enters of Triangles acket13 32) Name the 3 properties of the circumcenter, and provide diagrams to help you study. a] b] c] 33) Name 2 properties of the centroid, and provide diagrams to help you study. a] b]

14 enters of Triangles acket14 34) Name 1 property of the orthocenter, and provide a diagram to help you study. a] 35) Which of the following is NOT true about the incenter? (1) It is equidistant from the triangle s 3 sides. (2) It is the point of concurrency of the triangle s 3 angle bisectors. (3) It is the center of the triangle s inscribed circle. (4) It is the center of the triangle s circumscribed circle. 36) Which of the following is NOT true about the circumcenter? (1) It is the center of the triangle s circumscribed circle. (2) It is the point of concurrency of the triangle s 3 perpendicular bisectors. (3) It is equidistant from the triangle s 3 vertices. (4) None of the above. 37) Which of the following is NOT true about the centroid? (1) It is the point of concurrency of the triangle s 3 medians. (2) It divides each median into a ratio of 1:2 (3) It is located 2/3 of the way from each vertex to its opposite side. (4) It is located 2/3 of the way from each side to its opposite vertex.

15 enters of Triangles acket15 38) What does the point G represent? State 3 facts about it. 39) Will the always be inside the triangle? 40) What does the point G represent? State 2 facts about it. E G F D 41) Will the always be inside the triangle?

16 enters of Triangles acket16 42) What does the point Z represent? State 3 facts about it. Z 43) Will the always be inside the triangle? 44) What does the point H represent? How did you know? 6) How do you know 45) Will the always be inside the triangle?

17 enters of Triangles acket17 46) Identify the center shown in each diagram, and explain how you knew. 47) onsider the diagram below: a] What is the point G called? b] It must be that (TRUE / FLSE) c] It must be that (TRUE / FLSE) d] It must be that (TRUE / FLSE) e] If, and, what is?

18 enters of Triangles acket18 48) onsider the diagram below: S a] What is the point called? b] It must be that (TRUE / FLSE) R Q c] It must be that (TRUE / FLSE) d] would be located outside of the triangle if the triangle was (1) acute (2) obtuse e] If this were a right triangle, then would be located: (1) On the hypotenuse of the triangle (2) On the vertex of the right angle of the triangle 49) onsider the diagram below: a] What is the point S called? b] If, find and. c] If, find and. d] It must be that (TRUE / FLSE) e] It must be that (TRUE / FLSE)

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