MTHSC 118
Lab 14: Similar Triangles
Name
SN
March 9, 2010
1.
Go to page “Similar Triangles.”
2.
Drag point D and E to change the blue triangle. As you drag the points, what
changes and what stays the same?
3.
Press Blue to Yellow. Then press Yellow to Blue. What does this seem to
show about the two triangles?
4.
To change the shape of the yellow triangle, first press Show Vertices. Drag
the vertices of each triangle. Observe what changes and what stays the
same.
5.
Drag point D and E until VDEF lies exactly on top of VABC . Where do you
have to place point D and E to make the triangles match up?
6.
Drag the triangles apart again. Make CAB in the yellow triangle very small.
What happens in the blue triangle?
7.
Drag point C far away from points A and B. What happens in the blue
triangle?
8.
Press Show Angle Measurements. Drag each vertex to see what happens to
the angle measurements. Which angle in the blue triangle corresponds to
ABC in the yellow triangle?
Adapted from Sketchpad LessonLink
Lab 14: Similar Triangles
March 9, 2010
9.
Which angle corresponds to BCA ?
10.
Which angle in the yellow triangle corresponds to FDE ?
11.
What can you conclude about the corresponding angle of similar triangles?
12.
How many angles are needed to show two triangles are similar?
13.
Select each side and chose Measure | Length.
14.
Calculate the ratio of one pair of corresponding sides. To do so, choose
Number | Calculate to open the Sketchpad Calculator. Click on a
measurement to enter it into a calculation.
15.
Calculate the ratios of the other two pairs of corresponding side lengths.
What can you conclude about the ratios of the corresponding side lengths of
these triangles?
16.
Complete the following proportion using the ratios you calculated in steps 14
and 15. Then rite two other proportions using these ratios.
AB
17.

DF
If AB=3.0 cm, BC=4.0 cm, and DE=5.0 cm, use the triangles to find EF. Set
up a proportion to check your answer.
Adapted from Sketchpad LessonLink
Lab 14: Similar Triangles
March 9, 2010
17.
Go to page “Rules for Similarity.” From Steps 11 and 12, what can you say one
similarity rule might be?
18.
Press SSS and follow the instructions on the screen. Is triangle DEF similar
to triangle ABC?
19.
Press SAS and follow the instructions on the screen. Is triangle DEF similar
to triangle ABC?
20.
Press SSA and follow the instructions on the screen. Is triangle DEF similar
to triangle ABC?
21.
Add a new page and label it “Tree and Shadow.” Go to File | Document
Options, and click Add Page | Blank Page naming your page “Tree and
Shadow.”
22.
Draw a horizontal line to represent the ground. Holding down the Shift key
makes it easier to make the line horizontal.
23.
Select the control points of the line and choose Display | Hide. You should
now see only the line.
24.
Construct two points on the line. These will represent your feet and the
bottom of the tree.
25.
Select the points and the line and choose Construct | Perpendicular Lines.
26.
Construct segments on these lines that start at the ground and go up.
27.
Hide the original line under your segments.
28.
Label the lines. Double-click the labels and change them to You and Tree.
29.
Construct a ray from above and to the right of the tree, down to the ground.
This ray represents a ray of sunlight.
Adapted from Sketchpad LessonLink
Lab 14: Similar Triangles
March 9, 2010
The sun is so far away and large that its rays are essentially parallel when they
reach the Earth. In steps 30 through 32, you’ll construct lines parallel to the ray
of sunlight and segments representing your shadow and the tree’s shadow.
30.
Select the ray and the points representing the top of you and the tree, and
choose Construct | Parallel Lines.
31.
Construct the points where the parallel lines intersect the ground.
32.
Construct segments to represent you shadow and the tree’s shadow. Change
the line width to thick and label the shadows.
33.
Measure the three things that you would be able to measure in real life: your
height and the lengths of both shadows.
34.
Use these measurements to calculate the height of the tree.
Adapted from Sketchpad LessonLink