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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 - Building Confidence

NameDate

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

  1. Kira draws triangle DFH. Segment DQ runs from vertex D to Q, the midpoint of side FH, and does not meet FH at a right angle. What is DQ called?

    • a perpendicular bisector
    • an angle bisector
    • a median
    • an altitude

  2. Luz draws triangle DFH. Segment FS runs from vertex F to side DH and meets DH at a right angle, but S is not the midpoint of DH. What is FS called?

    • an angle bisector
    • a perpendicular bisector
    • a median
    • an altitude

  3. Milo draws triangle DFH. Segment HU runs from vertex H to U on side DF and splits ∠DHF into two equal angles. What is HU called?

    • an angle bisector
    • a perpendicular bisector
    • an altitude
    • a median

  4. Noah draws triangle DFH. Line WQ crosses side FH at its midpoint Q, makes a right angle with FH, and does not pass through vertex D. What is WQ called?

    • an altitude
    • a median
    • a perpendicular bisector
    • an angle bisector

  5. Ren plans a triangular flower bed DFH and marks its centroid G. Median DQ is 36 inches long. How long is DG, in inches?

  6. Tala studies the triangular front DFH of a tent and marks its centroid G. Median DQ is 45 cm long. How long is DG, in cm?

  7. Zee draws the triangular sail DFH of a model boat and marks its centroid G. Median DQ is 54 inches long. How long is DG, in inches?

  8. Bo draws triangle DFH and the perpendicular bisectors of the three sides. They meet at point O. What is point O called?

    • the incenter
    • the centroid
    • the circumcenter
    • the orthocenter

  9. Esme draws triangle DFH and the three angle bisectors. They meet at point I. What is point I called?

    • the incenter
    • the circumcenter
    • the centroid
    • the orthocenter

  10. Jun draws triangle DFH and the three altitudes. They meet at point Y. What is point Y called?

    • the orthocenter
    • the incenter
    • the circumcenter
    • the centroid
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10th grade Medians, altitudes and bisectors: name them, and find where they meet worksheet – printable
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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.

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