LESSON PLAN (Linda Bolin) - Granite School District

LESSON PLAN (Linda Bolin)
Lesson Title: Finding Missing Lengths of Similar Triangles
Course: Pre-Algebra Date January Lesson 4
Utah State Core Content and Process Standards:
2.3b Identify pairs of similar triangles using two pairs of congruent angles, or two pairs of
proportional sides with congruent included angles
2.3c Find missing lengths of similar triangles, including inaccessible lengths, using
proportions
Lesson Objective(s): Identify triangles as similar or not and use proportions to finding
missing lengths of similar triangles.
Enduring Understanding (Big Ideas):
If two figures are similar, corresponding
angles are congruent and corresponding
sides are in proportion.
Essential Questions:
• How can a proportion be used to find missing
lengths of sides in similar triangles?
• How can similar triangles be used to find
inaccessible lengths?
Skill Focus:
Find missing sides of similar triangles
using a proportion
Vocabulary Focus:
Similar triangle, corresponding angles,
corresponding sides
Materials:
• Overhead of figures for the Similarity Basketball Game
• Trash can or box for basketball goal, and a foam ball. Masking tape for shooting line.
• Sketching Similar Triangles Rally Coach worksheet
• Similar Triangles-Finding Missing Measures, rulers
• Solving Height Problems Using Similar Triangles
Assessment (Traditional/Authentic): observation, questions, performance task
Ways to Gain/Maintain Attention (Primacy): sketching, games, hands-on, discussion
Written Assignment:
• Similarity Basketball record
• Worksheets: Sketching Similar Triangles Rally Coach, Similar Triangles-Finding Missing
Measures, Solving Height Problems Using Similar Triangles
List the vocabulary on the board
Starter: 15’
Content Chunks
3’ 1. Are the two rectangles similar? Explain.
6’ 2’
6 cm
2. Are the two triangles similar? Explain.
3 cm 9cm
2 cm

Lesson Segment 1: Identifying similar figures Using A Proportion
Since the corresponding sides of similar figures form equivalent ratios, a
proportion equation can be used to check whether or not two figures are similar.
Explain and model for students how a proportion can be used to check for equivalency
by identifying a two pairs of corresponding sides, setting up the ratios, and using cross
products to check for proportionality.
Game: Similarity Basketball
Set up the trash can or a box for a basket. Place three different pieces of tape on
different places on the floor all about 8 feet from the basket. Use a foam ball or
wadded up paper ball. Divide the class into two teams: A and B. On the overhead,
show one of the pairs of figures below. Ask students to use their knowledge about
similar figures and a proportion to help them determine whether the figures are similar
or not. On their paper, they should sketch and label each pair, and then determine
similarity. After giving them time to put their ideas on their paper, have them check
with a buddy to confirm their reasoning. Then, call on one student from a Team A to
answer and explain. If the student is correct, they come to shoot a basket, or ask a
team mate to shoot for them. The shooter may choose any tape mark they want to
shoot from. The basket is worth 2 points. If the student is not correct, the other team
gets to shoot a foul shot for 1 point. Clarify and correct all errors and have the
students make corrections on their papers. Teams take turns answering and shooting.
Figures for Basketball Game:
3
9 12 2
6 4
4 6 6
6 8 4
4
10 12 15
3 2 20
5
16
3
4.5 20

Lesson Segment 2: How can a proportion be used to find missing lengths of
sides in similar triangle.
Give each pair of students one Sketching Similar Triangles Rally Coach worksheet
to look at. Q. How might proportions be used to help you determine how long to make
the corresponding side of the missing triangle on this page? Discuss and model a
number 1 and 2 helping students count, set up proportions, solve, and sketch
Rally Coach: Divide students into pairs to complete # 3-6 on the Sketching Similar
Triangles Rally Coach worksheet. One partner takes the role of coach explaining to the
other what needs to be done and why. The other partner takes the role of player.
The player decides whether or not to follow the coach’s advice and works the problem
on the paper they share. For the next problem, the roles are reversed. The students
take turns being coach and player as they complete the worksheet. Both names must
be on the paper. You may need to have one group of three where they all take turns.
Four Corners: When we can’t count, we can use the given measures of sides of
similar triangles to help us find missing measures. Model using these.
5 s
4
6
Give each student the Similar Triangles-Finding Missing Measures worksheet. Have
each student from a team go to a different corner of the room depending on their
number (1-4) to meet with other students having that same number. In the corner,
they work with others to solve one of the problems. Persons # 1 does problem # 1.
Person # 2 does problem # 2. Person # 3 does problem # 3. Person # 4 does
problem # 4. Give them enough time to make sure every person in a corner can
explain how to set up and solve the problem using a proportion. Students go back to
their home teams where they take turns teaching their team members the problem
they did in the corner.
Lesson Segment 3: How can similar triangles be used to find inaccessible lengths?
Have student pairs form similar triangles using a mirror to find inaccessible heights.
Set mirror on the floor in front of a student. The student back away from mirror until
the inaccessible object becomes visible. Partner measures the student’s height, the
distance the student is from the mirror and the distance the mirror is from the object.
They set up proportion to find the height of the object. Then repeat using the partners
height. See Solving Height Problems Using Similar Triangles worksheet.
Assign text practice as needed.

Names: _______________________
_______________________
Sketching Similar Triangles
Rally Coach
For each problem on the grid below, a triangle has been sketched for you. A
corresponding segment of a similar triangle has also been sketch. Use a proportion to
determine how long a second corresponding side should be, and then sketch the similar
triangle. Line segment AB corresponds to line segment DE in each problem.
D
1. 2. D E
A
B
E
A
B
3. A B 4. A D E
D
E
A
B
5. D 6.
A
D
B
E
B E C
7. Sketch two similar triangles
using a scale factor of 2.

Similar Triangles, Finding Missing Measures
Name_______________
Date _________
Use a proportion to find the length of segment s in each similar pair.
1. 2.
2.1
5 s 3.4
10.2
3 4.5
S
3. 4.
2
10 8
15
5
s 4
For the following problems, use decimeters on a ruler to measure.
5. These triangles are similar. Measure A
segment AB. Measure segment DE.
Write the ratio of AB/DE. Measure
segment BC. Set up a proportion to find
the length of segment EC.
D
B E C
6. These two triangles are similar. Measure
segment FH. Measure segment IJ. Write
the ratio of FH/IJ. Measure segment GJ.
Set up a proportion to find the length of
segment FG.
F
G
I
H
J

Solving Height Problems Using Similar Triangles
Name________________
Date _________
Find an object’s height indirectly, by using similar Triangles
Materials needed: a yardstick, a mirror, a partner.
Procedure:
1) With a partner, measure your height in inches to the nearest half inch.
2) Choose an object in the room. Lay the mirror on the floor so the center of the
mirror is 36” from the object. Leave the mirror in place on the floor. Back away
from the mirror until you can see the top of the object in the center of the mirror.
3) Measure the distance from the arch of your foot to the center of the mirror.
4) Use this data to set up a proportion for finding the height:
a) Your height,
b) Distance object is from mirror center
c) Distance you must stand from mirror center to see the top of the object
Object
Set up and solve a
proportion to find height
Height of object