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Acute, Obtuse, and Right Triangles

This is a free geometry lesson for 4th grade about acute, obtuse, and right triangles (classification according to angles). It contains varied exercises, including several where students explore these concepts -- and even the angle sum of a triangle -- by drawing.

  

right angles
(exactly 90°)

 

obtuse angles
(more than 90°, less than 180°)

acute angles
(less than 90°)

 
Right triangles have
exactly one right angle.

 

 Obtuse triangles have
exactly one obtuse angle.

Acute triangles have three
acute angles. In other words,
ALL the angles are acute.

 

1. a. Draw a right angle. Then
        make it into a right triangle
        by drawing in the third side. 
 

     b. Draw another, different
         right triangle.

 

   c. A right triangle has one right
       angle. Are the other two angles
       in a right triangle acute, right,
       or obtuse?

 

 

 

 

 

 

A right triangle has one right angle. The other two angles are _____________________.


2. a. Draw an obtuse angle.
        Then make it into an
        obtuse triangle by
        drawing in the third side.
 




 

 
   

    b. Draw another, different
        obtuse triangle.

    c. An obtuse triangle has one
        obtuse angle. Are the other
        two angles in a obtuse triangle
        acute, right, or obtuse?


 

 

 

An obtuse triangle has one obtuse angle. The other two angles are _____________________.

 

3. a. Draw an acute triangle.
        The side lengths can be any.

    b. Measure its angles.
        They measure _______°,
        _______°, and _______°.
 


 

 

4. Observe all you have done thus far in this lesson, and fill in.

Right triangles have exactly 1  _________________    ________________,

and the other two angles are _________________ .

Obtuse triangles have exactly 1  _________________    ________________,

and the other two angles are _________________ .

Acute triangles have ___    ____________ angles.



5. Label the triangles in the pictures as right, acute, or obtuse.

a.
 

b.
 

c.
 

d.
 

e.

 

f.

 

g.

 



7. a. Draw a triangle with
        85° and 40° angles.

         Hint: First draw a 85° angle.
         Then, mark a point anywhere on one
         side of that angle to be the second
         vertex of the triangle. Use that point
         as a vertex for the 40° angle, and
         draw the 40° angle.

    b. Measure the third angle.
        It is _______ degrees.

    c. What kind of triangle is it?
        (acute, right, obtuse)

    d. What is the angle sum?

 

 

   



8. a. Draw a triangle with
        125° and 40° angles.

    b. Measure the third angle.
        It is _______ degrees.

    c. What kind of triangle is it?
        (acute, right, obtuse)

    d. What is the angle sum?
 
 

 
   

9. a. Draw a triangle with
        55° and 35° angles.
 

    b. Measure the third angle. 
        It is _______ degrees. 

    c. What kind of triangle is it?
        (acute, right, obtuse)

    d. What is the angle sum?

 

 



This lesson is taken from Maria Miller's book Math Mammoth Geometry 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.



Math Mammoth Geometry 1

A self-teaching worktext for 4th-5th grade that covers angles, triangles, quadrilaterals, cirlce, symmetry, perimeter, area, and volume. Lots of drawing exercises!

Download ($6.90). Also available as a printed copy.

=> Learn more and see the free samples!

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