Name:
GEOMETRY
AND
SPATI AL SENSE: TY PES
OF
T R I A N G L E S (B Y S I D E S )
1. By sides, which type of triangle does each of the following appear to be?
REMEMBER
An
equilateral
triangle has three
equal sides.
An
isosceles triangle has
two equal sides. A
scalene triangle has
three unequal sides.
2. Within each box, three of the triangles are the same type by sides. Shade the triangle that is different.
3. a) Use your ruler to neatly draw and label:
i)
ABC with BC = 3 cm,
ii) DEF with DE = 4 cm,
AB = 4 cm, and AC = 5 cm.
EF = 4 cm, and DF = 6 cm.
b) State the type of each of these triangles by sides.
i)
ii)
Expectation: i) identify and construct triangles, and classify them according to side properties
iii)
iii)
GHI with GH = 5 cm,
HI = 5 cm, and GI = 5 cm.
4. Please follow your teacher’s instructions to open The Geometer’s Sketchpad
and maximize your screen. If 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 four triangles that appear to be:
a) scalene. Clear the screen.
b) isosceles. Clear the screen.
c) equilateral. Clear the screen.
6. 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 at least 5.0 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) Use the line segment tool to draw AC. Measure the length of AC. 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) Select B, A, and C in that order. Click on the Measure menu and choose Angle. Click on empty space.
l) Choose the selection tool. Drag C until ABC = 90° and BAC = 45°.
m) The length of AB is
. The length of BC is
.
n) By sides, what kind of triangle is ABC?
o) Select and delete both ABC and the measurements.
Note: To change the name of a point, double click on the letter and change the letter.
7. Repeat question 6 (steps d to o) to construct:
a) DEF so that DEF = 30° and EDF = 60°.
The size of DFE is
.
The length of DE is
.
The length of EF is
.
The length of DF is
.
DEF is a(n)
triangle.
b)
TRY THIS!
At the right, all of the triangles are either equilateral or
scalene. Colour each equilateral triangle red, each
scalene triangle brown, and each quadrilateral blue.
What animal have you coloured?
Expectation: i) identify and construct triangles, and classify them according to side properties
GHI so that GHI = 60° and HGI = 60°.
The size of GIH is
.
The length of GH is
.
The length of HI is
.
The length of GI is
.
GHI is a(n)
triangle.