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Science Math Masters
Summer Workshop: June 17th – June 20th
Group Lesson: Similarity, Right Triangles, and Trigonometry (SRT)
MACC.912.G-SRT.1.1 Verify experimentally the properties of dilations given by a center and a scale factor:
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center
unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
MACC.912.G-SRT.1.2 Given two figures, use the definition of similarity in terms of similarity and transformations to decide if they are similar;
explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides.
MACC.912.G-SRT.1.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Part One: Warm-Up
Solve for the variable. Round all answers to two decimal places if necessary.
1.
5 9
=
x 4
2.
8
4
=
11 x -1
Complete each congruence statement given that
4. PC @ _____
3.
2x +1 x + 2
=
13
9
.
5. ÐHDL @ _____
Show work to justify your answer.
6. A cell phone is approximately 4.6 in wide and 8.4 in long. What is the ratio of the width of the cell
phone to the length?
7. A bonsai tree is 18 in. wide and 2 ft tall. What is the ratio of the height of the bonsai tree to its width?
Part Two: Hook/Motivation for Lesson
Video clip
You will work in groups to record the measurements in the table and on the figure below. Use a
protractor to measure the angles. Round to the nearest angle measure. Figures are not drawn to scale.
FIGURE 1
FIGURE 1’S MEASUREMENTS
Angle Measures
2.5
mÐL
mÐM
mÐN
mÐJ
mÐK
2
1.5
3.2
Side Lengths
JK =
KL =
LM =
MN =
NJ =
3.5
FIGURE 2
FIGURE 2’S MEASUREMENTS
Angle
S Measures
10
8
6
12
14
mÐR
mÐS
mÐT
mÐP
mÐQ
Side Lengths
PQ =
QR =
RS =
ST =
TP =
1. What do you notice about the angle measures of the two figures?
a. Which angles have a relationship within the figures?
b. Why do you think these angles have this relationship?
Use the information from your figures to find the following ratios in simplest form:
RATIO
JK
PQ
KL
QR
LM
RS
MN
ST
NJ
TP
2. State any observations made from your ratios.
a. Why do you think these sides have this relationship?
3. The three figures provided are similar figures. Make a conjecture about the properties of similar
figures.
**Teacher note: After all groups have made their conjectures have each group record their data on chart
paper (provided). Groups walk around and test their conjecture based on others group data/students
present their data via document camera for groups to test conjecture. Show powerpoint slides on sim.
Student notes:
4. Write a similarity statement for your groups’ three figures.
Find the missing side(s) for each polygon. Figures are not drawn to scale.
5. ABGE~CDHF
5
3
6
y
z
6
9
15
Determine which pair(s) of triangles are similar. Write the similarity statement for the similar
triangles. Identify the scale factor(s).
6.
7. A woman’s shadow and a tree’s shadow form similar triangles. The length of the woman’s
shadow is 3 feet and the length of the tree’s shadow is 7.5 feet. If the woman is 5.5 feet tall, how
tall is the tree? Round your answer to the nearest tenth, if necessary.
Revisit capitol building dimensions. Legoland model is 7 feet tall. Actual capital building is 19 feet 6
inches. Find the scale factor.
Return to video clip: capitol building summaryPossible Extension: Given coordinates and a scale factor of a quadrilateral, students will be asked to
draw a similar figure using the given scale factor.