Medians, altitudes and bisectors: name them, and find where they meet
Grade 10 Math Worksheet
Circle the best answer, or write your answer on the line.
Kira cuts a sandwich into triangle DFH with centroid G on median DQ. DG = (4x − 12) cm and GQ = (x + 9) cm. How long is DQ, in cm?
Luz draws ramp side DFH with centroid G on median DQ. DG = (5x − 5) inches and GQ = (x + 11) inches. How long is DQ, in inches?
Milo traces watermelon slice DFH with centroid G on median DQ. DG = (5x − 1) cm and GQ = (2x + 5) cm. How long is DQ, in cm?
Noah traces cheese wedge DFH with centroid G on median DQ. DG = (6x − 12) inches and GQ = (x + 8) inches. How long is DQ, in inches?
Pia leans a ladder on a wall, making right triangle DFH with the right angle at F. Where is the circumcenter of triangle DFH?
- at F, the vertex of the right angle
- outside the triangle
- at the midpoint of the hypotenuse, DH
- inside the triangle
Ren marks three towns on a map, making triangle DFH with an obtuse angle at F. Where is the circumcenter of triangle DFH?
- outside the triangle
- inside the triangle
- at the midpoint of the longest side, DH
- at F, the vertex of the obtuse angle
Tala draws the side of a ramp as right triangle DFH with the right angle at F. Where is the orthocenter of triangle DFH?
- outside the triangle
- at F, the vertex of the right angle
- at the midpoint of the hypotenuse, DH
- inside the triangle
Zee draws the front of a wide tent as triangle DFH with an obtuse angle at F. Where is the incenter of triangle DFH?
- outside the triangle
- inside the triangle
- at F, the vertex of the obtuse angle
- at the midpoint of the longest side, DH
Ari marks three towns on a grid map: D(1, 2), F(7, 4) and H(4, 9). What are the coordinates of the centroid of triangle DFH?
Bo plans three park lamps on a grid: D(2, 1), F(8, 3) and H(5, 11). What are the coordinates of the centroid of triangle DFH?