3rd Grade - Isosceles, Equilateral And Right Triangles

Shapes and Geometry
Isosceles, Equilateral and Right Triangles
Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).
Measurement and Geometry: triangles, isosceles, equilateral, right angle The ability to classify different types of triangles and sort them based on defining characteristics.

Sample Problems


What makes triangles different from each other?

Triangles can be classified by their attributes, such as angles (right, acute, obtuse), sides (equilateral, isosceles, scalene), and size (similar and congruent).


Do the angles matter when sorting triangles?

Angles: right triangles have one right (90 degree) angle. Acute triangles have all angles less than 90 degrees. Obtuse triangles have one angle more than 90 degrees.


What is the significance of the length of a triangle’s sides?

Sides: Equilateral triangles have all three sides the same length. Isosceles triangles have two sides that are the same length. Scalene triangles have all three sides different lengths.


Can triangles be different sizes?

Size: Similar triangles have the same shape, but they may be different sizes. Congruent triangles have the same size and shape.


Can triangle shapes be put together to make other things? Yes, triangles fit together to make all kinds of other shapes.

Learning Tips


Students can model acute, obtuse and right angles using their elbow joint. An index card corner or a corner of paper can be used as a check point to determine whether an angle is a right angle or not. Children can use the index card to check different angles that are drawn on a piece of paper or that exist around the house.


Symmetry: explore symmetry by asking children to fold a heart in half and talk about congruency (each side matches perfectly). The line along the fold is called the line of symmetry. Different letters of the alphabet can be written and children can determine which are symmetrical. Children can also fold a equilateral triangle in half and talk about symmetry.


Allow your child to use 3 pushpins, a bulletin or corkboard at a comfortable height (or on the table) and a few rubber/elastic bands to create triangles. Let your child tell you and show you what a right triangle looks like; he/she will learn more if you allow that child to decide where to put the pushpins and how to stretch the elastic around the pins. Ask your child to “prove” to you that a right triangle has been made by using a square corner to match the triangle’s right angle. Equilateral triangles have three equally-long sides; find some sort of linear measuring tool (a ruler, a paper that can be marked, etc.) to assist in moving the pins until all 3 sides are equal in length. An isosceles triangle has 2 equal sides; ask your child to move the pins until an isosceles triangle can be created. Praise your child for working out these problems with patience; a lot of “trial and error” is involved.


Did your child’s triangles look pretty much like “textbook examples” of triangle types? The usual format is that the steepest angle is at the top; it’s rare to see triangles in math books and worksheets to show any other arrangement. So that your child will have a more flexible view, challenge your child to create a right triangle with the right angle at the top of the board. Similarly, ask your child to create an isosceles triangle that looks more like an ice-cream cone (if by some chance this is the way your child created the earlier triangles, ask for another layout) and then ask him/her to create some designs on the board, using more pushpins and rubber bands. Challenge him/her to have all of the triangles touch each other in the design.


Ask your child to create an isosceles or equilateral triangle. You can do this with the pushpins/elastics or draw it on paper. The challenge here is to use only one line, or only one extra elastic band, to change the single triangle into two right-angled triangles. Don’t help! Let your child figure it out and then describe to you how it was done. (A line/band dropped straight from the point that is centered over one of the lines to that line’s center will create a right angle on each side of the new line and there will be 2 right triangles inside the lines of the isosceles or equilateral triangle.

Extra Help Problems


Name 3 things in your environment that look like acute triangles.


Name 3 things in your environment that look like obtuse triangles.


Name 3 things in your environment that look like equilateral triangles.


Draw a triangle on your paper. Draw a second triangle that is different in some way. How are they different? Describe in just a couple of words. Draw a third and say how it is different. 90/39/51


Draw a right triangle. The lines extending from the right angle should be 3 inches and 4 inches. After you draw the third line, measure it. About how long is it? (5 inches)


Is it possible to draw a right triangle that is obtuse? If so, do it.


Is it possible to draw an isosceles right triangle? If so, do it.


Is it possible to draw a scalene right triangle? If so, do it.


Is it possible to draw an equilateral right triangle? If so, do it.


What are three ways to classify triangles? (size, angles, sides)


All three of my sides are the same length. What kind of triangle am I? (equilateral)


I am an angle less than 90 degrees. What am I called? (acute angle)


I am an angle more than 90 degrees. What am I called? (obtuse angle)


All of my sides are different lengths. What kind of triangle am I? (scalene triangle)


I am a triangle with one right angle. What kind of triangle am I? (right triangle)


I am a triangle with one of my angles at 105 degrees. What kind of triangle am I? (obtuse triangle)


I am a triangle with one angle at 60 degrees, 80 degrees and 35 degrees. What kind of triangle am I? (acute triangle)


Two of my sides are the same length. What kind of triangle am I? (isosceles)


Draw 2 congruent triangles.


Draw 2 similar triangles.


Draw two different looking congruent triangles than you did above. What makes them congruent?


Draw two different looking similar triangles than you did above. What makes them similar?


Draw a rectangle of any size. Draw a diagonal line between any two angles. What shapes have you made? (2 right triangles)


Inside the rectangle that you made in problem 3, connect the opposite angles that you didn’t connect before. How many small triangles are formed? (4) How many triangles in total are now inside your rectangle? (There could be as many as 8! See how many you can find.)


Draw a house. Your house can only be made of triangles. When you are finished, ask someone to count how many triangles you were able to use. Don’t forget to count the triangles that happen to be inside other triangles!


Draw an equilateral triangle. Cut it out. Use this triangle as a pattern to draw several more and cut those out, too. Arrange your triangles in a shape where all of the tall points of your triangle meet together in the center. How many triangles does it take to fill in a shape so that no part of your work surface shows?


Try the same activity as #5, above, but use isosceles triangles instead. Does the number of triangles needed to complete the structure change when the type of triangle is changed? (Answers vary; let your child draw his/her own conclusions)


Try this exercise with various sizes of isosceles triangles. All of the triangles for one design must be the same size, but you can make the two long sides much longer, or much shorter, than the first one you made. Again, arrange your triangles so that all of the tall points meet in the center of a circular-type design. Does the number of triangles needed vary with the size of the triangle sides? (Answer will vary, depending on how your child sizes his triangles)


Use your pushpins and elastic band and try to create a triangle whose perimeter (the distance around the triangle’s sides) is 10 inches. (It might be easiest to use a strip of paper or string that is 10 inches long to measure around your triangle.) Keep moving your pins until you have a perimeter as close to 10 inches as possible. Show someone your triangle and tell about how you created it.


Draw an animal whose body parts are all triangles. Name your animal! How many triangular body parts did you manage to give your animal?


Draw another animal using these rules: You must use at least one of each type of triangle (right, isosceles, equilateral). You must also use the same number of each triangle type. For example, if you use 3 right triangles you must use 3 each of the other types too. Show your animal to someone and compare it with the first animal that you drew. When you are talking about your animal, be sure to use the correct names for your triangles.


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