Math 3305, Chapter 3 Similarity
Activity pages A
Name:
Activity pages – print full size, one side only. Staple, please, in advance.
Here’s a break for you. Sit beside someone new that you’ve met since class started and who
you’d like to get to know better. Exchange emails and phone numbers!
Points:
Printed and stapled
05 points
Similarity exercise 3 – 4 – 5 triangles
05 points
Nested triangles exercise
05 points
Three similar triangles exercise
12 points
Trig exercise 1
08 points
Supplemental Angle Conundrum
05 points
Reference angle chart
05 points
Total score: _________
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Similarity 3 – 4 – 5 triangles
Sketch a 3 – 4 – 5 right triangle with generous side space on the right and left. Using a scale
factor of 0.5, sketch a similar triangle on the left. Sketch a similar triangle on the right with a
scale factor of 3/2.
Be sure to do the work on the next page, too.
Review how you know they are similar.
Check out the perimeters and areas – where does “k” fit in?
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Review how you know similarity is an equivalence relation (see page 37 in the text)
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3.2 Applications of similar triangles
Nested triangles similarity exercise:
Given:
The two triangles are nested and the bases are PARALLEL. Begin in the lower
left and name the points A – E, so that AB is the base of the large triangle and EC is the base of
the nested triangle. Now discuss why triangle ABD is similar to triangle ECD.
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Three similar triangles exercise.
What are the three triangles. Sketch them. Set up two ratios per triangle pair…3 pairs in all
C
mACB = 90.00°
A
Theorem 3.3.2
D
B
SAS Similarity Theorem
If two triangles have two pairs of corresponding sides in the same ratio and if the included angles
determined by the pairs of sides are congruent, then the triangles are similar.
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Three similar triangles continued
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Trig exercise 1
16cm
A
11cm
Find the missing side length. Round to 2 decimal places.
Find the the sine for angle A, the cosine for angle A, and the tangent for angle A
Sin(A) = _____
Cos(A) = _____
Tan (A) = _____
Use your new calculator function to check the measure of angle A
Angle A measures _______ degrees.
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Supplemental Angle Conundrum
Draw a linear pair with an angle of 33 degrees on the right and an angle of 147
degrees on the left.
Find the sine and cosine of each angle. Now using those answers find the inverse
sine and inverse cosine of each of the four.
What happened? Let’s discuss why it happens!
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Here’s another reference angle chart for you to work with:
angle in
deg
0
30
45
60
90
angle in
rad
sine
cosine
tangent
Count off left to right starting with 0.
Count back right to left starting with 0.
Square root and divide by 2.
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Chapter 3 Activities B
Name:
Print and staple in advance
05 points
Law of Sines and Law of Cosines
12 points
Perimeter and Area exercise
06 points
New instructions for transformations
08 points
Points total: _________
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Law of Sines and Law of Cosines
Problem 1
Given triangle ABC, with the measure of angle A = 35 degrees, and the measure of angle B is 45
degrees. These are the base angles of the triangle. The measure of the side across from A is 3
cm and the measure of the side across from B is 4 cm.
Why is the length of the base NOT 5 cm and how long is it? Use the Law of Sines.
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Problem 2
Given an obtuse triangle with largest angle measuring 135 degrees. The leg lengths around this
angle are 8 cm and 10 cm. What is the length of the side across from the obtuse angle?
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Problem 3
Given triangle ABC, the measure of angle A is 60°, the length of BC is 3 , and the
length of AC is 2 . Find the measure of angle B.
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Perimeter and Area exercise
Triangle A has a perimeter of 15 inches. Triangle B is similar to triangle A and has a constant of
proportionality of k = 9. What is the perimeter of triangle B and what is the ratio of Side 1 in
Triangle A to its corresponding side in Triangle B?
Perimeter of B = _____
Ratio side on A to corresponding side on B = _____
Triangle M has an area of 100 square inches. Triangle P is similar to Triangle M and has an area
of 25 square inches. What is the constant of proportionality between these two…going from M
to P?
k=
Triangle F has an area of 10 sqft. Triangle C is similar to triangle F with a k = 3…what is the
area of Triangle C?
Area of C =
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Instructions for transformations
Put the origin at the center of the graph paper. Put a 3-4-5 triangle on the paper
with the right angle at the point (1,2) and the horizontal leg being 4 units.
Do a similarity transform of (1/2 x, ½ y). What has happened?
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Now do a similarity transform on the original triangle of (− x, − y).
Be sure to put your origin in the center of this graph paper! What happened?
Can you figure out the reflection across the origin that is showing.
Homework note:
lengths.
a regular polygon has congruent interior angles and congruent side
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