Medians, altitudes and bisectors: name them, and find where they meet

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Kira plans a park fountain O. O is the circumcenter of triangle DFH: OD = (3x + 5) m, OF = (5x − 7) m, OQ = 14 m. How long is OH, in m?

   23
2. 2.

   Luz hangs a bird feeder O. O is the circumcenter of triangle DFH: OD = (4x + 9) m, OF = (6x − 1) m, OQ = 18 m. How long is OH, in m?

   29
3. 3.

   Milo picks a meeting spot O. O is the circumcenter of triangle DFH: OD = (3x + 7) yards, OF = (7x − 9) yards, OQ = 12 yards. How long is OH, in yards?

   19
4. 4.

   Noah marks a town square O. O is the circumcenter of triangle DFH: OD = (8x − 9) m, OF = (5x + 12) m, OQ = 30 m. How long is OH, in m?

   47
5. 5.

   Pia plans a garden sprinkler. I is the incenter of DFH: IU = (4x − 3) cm, IV = (2x + 9) cm, ID = 35 cm. How far is I from DH, in cm?

   21
6. 6.

   Ren marks a tabletop point. I is the incenter of DFH: IU = (5x + 2) inches, IV = (3x + 10) inches, ID = 30 inches. How far is I from DH, in inches?

   22
7. 7.

   Tala hangs a room lamp. I is the incenter of DFH: IU = (2x + 15) feet, IV = (5x − 3) feet, ID = 37 feet. How far is I from DH, in feet?

   27
8. 8.

   Ari maps three towns, D, F and H, but the map lost town H; it shows: D(1, 5), F(4, 3) and centroid G(4, 7). What are the coordinates of H?

   (7, 13)
9. 9.

   Bo plans park lamps at D, F and H and has written down: D(3, 1), F(8, 8) and centroid G(7, 6). What are the coordinates of H?

   (10, 9)
10. 10.

    Jun marked triangle DFH on a grid, but only these points remain: D(5, 7), F(8, 1) and centroid G(8, 7). What are the coordinates of H?

    (11, 13)