# GSS5 Types of Triangles

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GEOMETRY                 AND        SPATIAL SENSE: TYPES                              OF   TRIANGLES

1. State the types of triangle, by angles and sides, which each of the following appears to be.

REMEMBER
By sides, triangles are
scalene, isosceles, or
equilateral.
By angles, triangles
are right, acute,` or
obtuse.

2. Within each box, three of the triangles are the same type. Shade the triangle that is different.

3. a) Use your protractor and ruler to neatly draw and label:
i) ∆ABC with AB = 6 cm,             ii) ∆DEF with  DEF = 110°,                                         iii) ∆GHI with GH = 4.5 cm,
 BAC = 30°, and AC = 6 cm.         EF = 4 cm, and  DFE = 20°.                                            HI = 4.5 cm, and GI = 4.5 cm.

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b) State the type of each of these triangles both by sides and by angles.
i)                                   ii)                                                            iii)

Expectation: i) identify and construct triangles, and classify them according to angle and side properties
you need practice using the selection        , line     , and point     tools, please print and complete
Introduction to The Geometer's Sketchpad. You can find this activity at mathfrog.ca.
5. Use Geometer’s Sketchpad to draw three different triangles that appear to be:
a) scalene.                    d)    right.
b) obtuse.                     e)    isosceles.
c) equilateral.                f)    acute.
6. Use Geometer’s Sketchpad to draw a triangle that is both:
a) scalene and acute.
b) isosceles and obtuse
c) scalene and right.
d) isosceles and right.
e) scalene and obtuse.
7. a) Click on the Edit menu and choose Preferences.
b) Change the Precision of Angle to units and the Precision of Distance to tenths.
c) Check both boxes                                         and click OK.
d) Select the line segment tool      . Draw any line segment.
e) Choose the selection tool      . Click on the Measure menu and choose Length.
f) Drag point B until the length of AB is 12.0 cm. Click on empty space.
g) Select the line segment tool again. Starting at B, draw another line segment.
h) Choose the selection tool. Click on the Measure menu and choose Length. Click on empty space.
i) Drag C until BC = 5.0 cm. Click on empty space.
j) Select A, B, and C in that order. Click on the Measure menu and choose Angle. Click on empty space.
k) Drag C until  ABC = 90° and BC = 5.0 cm.
l) Use the line segment tool to draw AC. Measure and record the length of AC.
m) By sides, ∆ABC is a(n)                     triangle. By angles, ∆ABC is a(n)              triangle.
n) Select and delete both ∆ABC and the measurements.
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Note: To change the name of a point, double click on the letter and change the letter.
8. Repeat question 7 (steps d to n) to construct:
a) ∆DEF such that DE = 7.0 cm, EF = 7.0 cm,                                         b) ∆GHI such that GH = 18.2 cm,  GHI = 45°,
and  DEF = 60°.                                                                    and HI = 10.7 cm.
The size of  DFE is                      .                                         The size of  GIH is                  .
The size of  FDE is                      .                                         The size of  IGH is                  .
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The length of DF is                       .                                         The length of GI is                   .
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By sides, ∆DEF is                         .                                         By sides, ∆GHI is                     .
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By angles, ∆DEF is                        .                                         By angles, ∆GHI is                    .
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TRY THIS!
Use Geometer’s Sketchpad to create a design using only:
a) right triangles.
b) isosceles triangles.
c) acute triangles.
d) equilateral triangles.
Remember to use the Measure menu to find lengths of lines and sizes of