# Equilateral, Isosceles, and Scalene Triangles

This 5th grade geometry lesson defines equilateral, isosceles, and scalene triangles, and has a variety of exercises, including drawing exercises, about these topics for students.

 If all three sides of a triangle are congruent (the same length), it is called an equilateral triangle. Equi- refers to things that are the “same” or “equal”, and lateral means “sided.” Think of it as a “same-sided” triangle. If just two of a triangle’s sides are congruent, then it is called an isosceles triangle. Think of it as a “same-legged” triangle, the “legs” being the two sides that are the same length. Mark the two congruent sides of each isosceles triangle: Lastly, if none of the sides of a triangle are congruent (all are different lengths), it is a scalene triangle. 1. Classify the triangles by     the lengths of their sides     as either equilateral,     isosceles, or scalene.     You can mark each     triangle with an “e,” “i,”     or “s” correspondingly. 2. Fill in the table by classifying the triangles labeled as (a), (d), (e), and (g) above as “acute,” “right,”
or “obtuse” (by their angles), and also as “equilateral,” “isosceles,” or “scalene” (by their sides).

 Triangle Classification by the sides Classification by the angles a d e g

 3. Plot the points, and connect them with line     segments to form two triangles. Classify     the triangles by their angles and sides.     Triangle 1: (0, 0), (4, 0), (0, 4)     ___________________________ and     ___________________________       Triangle 2: (5, 5), (1, 8), (9, 4)     ___________________________ and     ___________________________ 4. Plot in the coordinate grid an acute scalene triangle. 6. a. Draw a scalene obtuse triangle where one side is 3 cm and another is 7 cm.
Hint: Draw the 7-cm side first, then the 3-cm side forming any obtuse angle with the first side.

b. Measure the third side.
Compare your triangle to those of your classmates, or draw another one yourself.
Can you draw several different-looking triangles with this information,
or are they all identical (congruent)? 7. a. Draw an isosceles right triangle whose two sides measure 5 cm.
Hint: Draw a right angle first. Then, measure off the 5-cm sides. Then draw in the last side.

b. Measure the third side.  It is ____________ cm.
Compare your triangle to those of your classmates, or draw another one yourself.
Can you draw several different-looking triangles with this information,
or are they all identical (congruent)? 8. a. Draw any isosceles triangle.
Hint: Draw any angle. Then, measure off the two congruent sides, making sure they have the same length.
Then draw the last side.

b. Measure the angles of your triangle. They measure ________ °, ________ °, and ________ ° .

The angle sum is ________ ° .

9. Measure all the angles in the isosceles triangles (a) and (b).
Continue their sides, if necessary.

 a. b. _________ °, _________ °, and ________ ° .       The angle sum is ________ ° . _________ °, _________ °, and ________ °.       The angle sum is ________ ° .

What do you notice?

__________________________________________________________________________________

__________________________________________________________________________________ There are two angles in an isosceles triangle that have the same angle measure. They are called the base angles. The remaining angle is called the top angle. Can you find the top angle and the base angles in this isosceles triangle?

10. The angle at A measures 40°. Draw another angle of 40° at B, and then continue its side
so that you get an isosceles triangle with 40° base angles. Measure the top angle. It is _______ ° . The three angle measures add up to _______ ° . 11. a. Draw an isosceles triangle with 75° base angles. (The length of the sides can be anything.)
Hint: start by drawing the base side (of any length). Then, draw the 75° angles.

b. Measure the top angle. It is _______ ° . The three angle measures add up to _______ ° .

c. Compare your triangle to those of your classmates, or draw another one yourself.
Can you draw several different-looking triangles with this information, or are they all identical?

 14. a. Could an equilateral triangle be a right triangle?           If yes, sketch an example. If not, explain why not.

b. Could a scalene triangle be obtuse?
If yes, sketch an example. If not, explain why not.

c. Could an acute triangle be scalene?
If yes, sketch an example. If not, explain why not.

d. Could a right triangle be scalene?
If yes, sketch an example. If not, explain why not.

e. Could an obtuse triangle be equilateral?
If yes, sketch an example. If not, explain why not.

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!

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