Explore Similar Triangles Activity 1.1.1 Lesson 1

Grade 10 Applied Math
Unit 1
Lesson:
Lesson 1: Explore Similar Triangles Activity 1.1.1
Lesson 1: Explore Similar Triangles Activity 1.2.2
Lesson 2: Apply Similar Triangles Activity 1.2.3
Lesson 2: Apply Similar Triangles: Practice Problems
Lesson 3: Applications of Similar Triangles
Lesson 4: Pythagorean Theroem
Lesson 5: Review
Unit 1 Test
Date:
Completed
Level
Unit 1: Lesson 1
Introduction to Similar Triangles
1.1.1: Growing and Shrinking Triangles
Investigation
Find area and perimeter of the triangle (Label it Triangle1)
If another triangle of the same shape has a perimeter that is double, what is the effect on the area
(Label it Triangle2)? If another triangle of the same shape has a perimeter that is half, what is the
effect on the area (Label it Triangle3)?
Hypothesis
Complete the investigation.
Calculate the area of each of the 3 triangles.
Atriangle1=
Atriangle2=
Atriangle3=
Calculate the perimeter of each of the 3 triangles.
Ptriangle1=
Ptriangle2=
Ptriangle3=
Consider the relationship:
Think of how to use ratios and proportions to calculate the relationship between:
 Triangle 1 and Triangle 2
 Triangle 1 and Triangle 3
Show you work.
Provide the conclusion:
Generalize by stating the relationship between the perimeter and the area of similar triangles.
Adjust your hypothesis, as needed.
Unit 1: Lesson 1
1.2.2: What Is Similarity?
1. a) On your geoboard create a right-angled triangle with the two perpendicular sides having
lengths 1 and 2 units.
b) Create two more triangles on your geoboard that are enlargements of the triangle created
in a).
2. Draw the three triangles using different colours on
grid and label the vertices, as indicated:
 triangle one (label vertices ABC)
 triangle two (label vertices DEF)
 triangle three (label vertices GHJ)
the
3. a) Determine the lengths of the hypotenuse of each of the triangles.
ABC
DEF
b) Indicate the length of each side of each triangle on the diagram.
GHJ
1.2.2: What Is Similarity? (continued)
4. a) Place ABC, DEF, and GHJ on the geoboard
so that the one vertex of each triangle is on the
same peg and two of the sides are overlapping.
b) Copy your model on the grid.
5. a) What do you notice about the corresponding angles of ABC, DEF, and GHJ?
b) What do you notice about the corresponding sides of ABC, DEF, and GHJ?
Summary
I know the following about similar triangles:
1.2.2: What Is Similarity? (continued)
6. Use the geoboards to explore whether the following triangles are similar.
a)
Explain your reasoning.
b)
Explain your reasoning.
c)
Explain your reasoning.
Lesson 2
1.2.3: Exploring Similarity
1. Which of the following four houses are similar? Explain why.
Label the diagrams.
Calculations:
2. On the grid, draw a house that is similar to one of the figures.
Complete the following statement:
The house I drew is similar to house #______.
I know this because:
1.3.1: Similar Triangles
Definition
Examples
Properties/Characteristics
Similar
Triangles
Non-examples
Practice Problems:
1. Complete the statements about the pair of similar triangles.
a)
d) 
b)

c)
e) 

f) 

2. Which two triangles are similar? You MUST show all your calculations AND justify your answer!
b) For the pair of similar triangles, state the pairs of corresponding sides and angles.
Unit 1: Lesson 3
Applying Similar Triangles
Practice Problems
Level 1:
1. A tall building casts a shadow 9.2 m long. At the same time, a 1.8-m tall person casts a shadow 0.4 m
long. How tall is the building? YOU MUST INCLUDE A DIAGRAM.
2. A loading ramp is built so that it rises 20 cm vertically for each metre horizontally. What is
the vertical height of the ramp shown in the diagram?
3. A park designer placed survey posts as shown in the diagram below. Measurements were made as
indicated. How far apart are the posts?
Level 2:
4. The top of a tree in your backyard needs pruning. The tree casts a shadow 4.5m long. At the same
time, your sister, who is 1.5m tall, casts a shadow that is 1.0m long.
a) Draw a diagram to represent this situation
b) How tall is the tree?
c) You are 1.7m tall and can reach 40cm above your head. Will you be able to prune the top of the tree
when you are standing on the top step of a 4-m ladder?
5. A triangle sign has sides of length 2.0m, 5.0m, and 6.3m. In a photograph of it, the smallest side is 1.5
cm long. How long are the other sides?
Level 3:
6. According to city by-law, backyard trees cannot be taller than 10m. Harold needs to determine if he
must prune the maple tree on his property. A 4-m tall post is held so that it is in line with the top of the
tree and it casts a shadow that is 2 m long. Harold’s tree casts a shadow that is 8 m long. How tall is the
tree? Does Harold need to prune the tree?
7. Orienteering is an important skill to learn in wilderness training. In one exercise, students walk due east
of the starting point. At the 3-km checkpoint is a refreshment stand. The next checkpoint is 5 km due east
of the first. From there, students must walk S220W to the third checkpoint.
In total, how far must the students walk to reach the third checkpoint?
Refreshment
Stand
3 km
5 km
Start
680
x
20 km
Checkpoint
End
Level 4:
8. A large conical paper cup is 20 cm tall and has a diameter of 8cm. Research shows that consumer find
the cup awkward to hold, so a new large cup will be designed. The new cup will be 4 cm shorter than, but
similar to the old one. What are the dimensions of the new large cup.
9. An Architect uses similar triangles to design a roof truss as shown. How far down from the tallest part
of the roof should the lower roof be fastened to the vertical support?
?
10m
5m
6m
10m
Unit 1: Lesson 4
The Pythagorean Relation
Practice Problems
Level 1:
Solve for the unknown
1a)
b)
Level 2:
2. If c is the hypotenuse, find the measure of b, given a = 6 and
. Draw the diagram.
3. A field measures 56 m by 89 m. How much shorter is it to walk diagonally across the field than along
two adjoining sides? Include a diagram.
4. A cordless telephone will work if it is within 50 m of its base. If, while you are talking on the phone, you
walk 15 m away from the base in a southerly direction, then, turn to face west and walk 42 m, will the
phone still work?
Level 3:
5. A 6-m pole is to be stabilized by tying 6.5 m of steel cable from a stake in the ground to a point 1 m from
the top of the pole. If 1 m of cable is to be used for tying purposes, how far from the base of the pole
should the stake be placed?
6. To meet safety standards, a wheelchair ramp must be built in the following proportion
Height: base length = 1 : 12
The wheelchair ramp at your school will be 0.9m high. What will be the length of the ramp along the
surface? Be sure to draw a diagram.
Level 4:
7. A tent frame is made as shown in the diagram. How long must the metal rods be to support the
roof?
rods
1.5 m
3m
8. A plane heads north, but as a result of wind currents, the plane is 40 km east and 200 km north of its
starting point. How far, to the nearest km is the plane from its starting point? Draw a diagram.
Unit 1: Lesson 5
Review
Practice Problems
Level 1:
1. Complete the statements about the pair of similar triangles:
a)
b)
c) ∠ABE = ∠
d) ∠ADC = ∠
2. Explain why the two triangles below are similar.
b) State the pairs of corresponding angles and sides.
3. Determine the length of the unknown side to one decimal place.
a)
b)
c)
e) ABE

4. A tree’s shadow is 3 m long. At the same time, a person who is 1.4 m tall casts a shadow that is 0.8 m
long. How tall is the tree?
5. The film in a pinhole camera is 6 cm in height. It is 8 cm from the pinhole. How far from the camera must
a 1.8-m tall person stand in order to be fully captured on film?
6. A rectangular field measures 120 m by 170 m. How much shorter is it to walk across it
diagonally instead of along two adjoining sides?
7. To find the width of a ravine, a large rock at point X on the opposite rim was used as a reference point
to take measurements as recorded on the diagram. Find the width of the ravine.

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