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

NameDate

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?
4.
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
- at the midpoint of the longest side, DH
- at F, the vertex of the obtuse angle
- inside the triangle
5.
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 the midpoint of the hypotenuse, DH
- at F, the vertex of the right angle
- inside the triangle
6.
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?
Esme plots three classrooms on a grid map of the school: D(0, 3), F(6, 0) and H(9, 9). What are the coordinates of the centroid of triangle DFH?
Jun draws triangle DFH on grid paper: D(3, 6), F(10, 2) and H(5, 4). What are the coordinates of the centroid of triangle DFH?

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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