# 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 haveexactly one right angle. Obtuse triangles haveexactly 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.

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