Grade 10 · Math · Geometry

10th grade Medians, altitudes and bisectors: name them, and find where they meet worksheet

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

Grade 10 Math Worksheet - Challenge Me

NameDate

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

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?
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?
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?
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?
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?
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?
Zee marks a sandbox point. I is the incenter of DFH: IU = (7x − 4) inches, IV = (3x + 20) inches, ID = 45 inches. How far is I from DH, in inches?
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?
Esme drew triangle DFH on grid paper, then erased H; left are: D(1, 5), F(5, 8) and centroid G(6, 8). What are the coordinates of H?
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?

10th grade Medians, altitudes and bisectors: name them, and find where they meet worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Medians, altitudes and bisectors: name them, and find where they meet. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can name a median, an altitude, an angle bisector and a perpendicular bisector, and the point where three of them meet.
I can say whether a triangle center is inside, on or outside a right or an obtuse triangle.
I can use the centroid's 2 : 1 split, find the centroid from coordinates, and use the equal distances of the circumcenter and the incenter.

Standard: G-CO.C.10, G-C.A.3, G-GPE.B.4

Words to know

median: A segment from a vertex to the midpoint of the opposite side.

altitude: A segment from a vertex that meets the opposite side at a right angle.

angle bisector: A segment from a vertex that splits that angle into two equal angles.

perpendicular bisector: A line through a side's midpoint at a right angle; it need not touch a vertex.

centroid: Where the three medians meet; it splits each median 2 to 1 from the vertex.

orthocenter: Where the three altitudes (or the lines they lie on) meet.

incenter: Where the three angle bisectors meet; the same distance from all three sides.

circumcenter: Where the three perpendicular bisectors meet; the same distance from all three vertices.

Common mistakes

Your child mixed up a median (to the midpoint of the opposite side) with an altitude (meets the opposite side at a right angle).

Your child mixed up a median with a perpendicular bisector; both pass through a midpoint.

Your child mixed up an altitude with a perpendicular bisector; both make a right angle with a side.

What to say

Ask: does it end at the middle, or meet the side square?

Ask: does the segment start at a vertex, and does it cross at a right angle?

Ask: does it start at a vertex, and does it cross at the midpoint?

Questions parents ask

What is the most common mistake with medians, altitudes and bisectors: name them, and find where they meet?

Your child mixed up a median (to the midpoint of the opposite side) with an altitude (meets the opposite side at a right angle).

How can I help my child with medians, altitudes and bisectors: name them, and find where they meet?

Ask: does it end at the middle, or meet the side square?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

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