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Transcript
```Lesson Design
Subject Area:
Geometry
9th – 12th
Benchmark Period
BM 3
Duration of Lesson: 2 days
Standard(s): Geometry 4b: Prove basic theorems involving similarity.
Learning Objective: Students will be able to identify similar triangles and prove two triangles are similar.
Big Ideas involved in the lesson:
Students will use similarity theorems to prove two triangles are similar.
As a result of this lesson students will:
Know:
Vocabulary: Ratio, proportion, similar, similarity, congruent, corresponding, corresponding parts.
Understand:
 If a and b are two quantities that are measured in the same units, then the ratio of a to b is
a
.
b
 Ratio is a quotient. The denominator cannot be zero.
 An equation that equates two ratios is a proportion.
Similar triangles: two triangles such that their corresponding angles are congruent and the lengths of
their corresponding sides are proportional.
Be Able To Do:
 Determine whether the triangles are can be proved similar.
 If triangles are similar, write a similarity statement.
Assessments:
What will be evidence of student
knowledge, understanding &
ability?
Justify why the two triangles are
similar.
Anticipatory Set:
a. T. focuses students
b. T. states objectives
c. T. establishes purpose of
the lesson
d. T. activates prior knowledge
1
Formative:
Observation, quiz, ABWA
Summative: CST &
Benchmark (DWA)
CFU Questions:
1. What is a conditional statement and how
do you write conditional statements using
similarity statement for angles, sides, and
triangles?
2. What are the measurements of the other
two angles?
3. What information do you need to
complete the following three problems?
Lesson Plan
Hands on Geometry:
Step 1: On a sheet of paper, use a ruler to draw a segment 2 cm in length.
Label the endpoints A and B.
Step 2: Use a protractor to draw an angle at A so that the measure of angle A
equals 87°. Draw an angle at B so that the measure of angle B equals 38°.
Extend the sides of angle A and angle B so that they intersect to form a
triangle. Label the third vertex C.
Step 3: Now draw a segment 4 cm in length. Label the endpoints D and E.
Lesson Design
Step 4: Use a protractor to draw an angle at D so that the measure of angle D
equals 87°. °. Draw an angle at E so that the measure of angle E equals 38°.
Extend the sides of angle D and angle E so that they intersect to form a
triangle. Label the third vertex F.
T. states, this lesson we will study two additional ways to prove that two
triangles are similar, Side-Side-Side (SSS) Similarity Theorem, Side-AngleSide (SAS) Similarity Theorem, and Angle-Angle (AA) Similarity Postulate.
T. reminds students they have learned how to use ratio and proportion to
determine similarity numbers, units, etc.
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for Understanding
 Pose key questions
concepts, definitions,
attributes in their own words
 Have students
discriminate between
examples and nonexamples
 Encourage students
generate their own
examples
 Use participation
Investigating Similar Triangles:
Have students use whiteboard, to complete the following steps:
Step 1: Use a protractor and a ruler to draw two non congruent triangles so
that each triangle has a 40 degrees angle and a 60 degrees angle.
Step 2: Measure the third angle, it will be 80 degrees.
Step 3: Label one triangle as ∆ABC and the other as ∆DEF.
Step 4: Measure the lengths of the sides of each triangle.
Step 5: Write and simplify the ratios of the corresponding sides.
T. explains: Similar triangles: two triangles such that their
corresponding angles are congruent and the lengths of their
corresponding sides are proportional.
T. asks: Are the triangles similar?
Discuss and justify as a class why the triangles are similar.
T. states: The symbol to signify similar triangles is “~”.
This activity are examples for Angle-Angle and Side-Side-Side.
Angle-Angle (AA) Similarity Postulate: If two angles of one triangle are
congruent to two angles of another triangle, then the two triangles are similar.
Side-Side-Side (SSS) Similarity Theorem: If the corresponding sides of 2
triangles are proportional, then the triangles are similar.
Side-Angle-Side (SAS) Similarity Theorem: If an angle of one triangle is
congruent to an angle of a second triangle and the length of the side including
these angles are proportional, then the triangles are similar.
CFU: Write conditional statements using similarity statement for angles, sides,
and triangles.
Do class poster, record similarity statements.
Guided Practice:
a. Initiate practice activities
under direct teacher
2
Refer to GeoCH0604example12.pps (use example 1) &
GeoCH0605example12.pps.
T. models how to solve problem 9 step-by-step along w/students at the same
Lesson Design
b.
c.
d.
e.
f.
supervision – T. works
problem step-by-step along
w/students at the same time
Elicit overt responses from
students that demonstrate
behavior in objectives
T. slowly releases student to
do more work on their own
(semi-independent)
Check for understanding
that students were correct at
each step
Provide specific knowledge
of results
Provide close monitoring
time. Have students work in pairs, and complete problems 10 & 11 on their
whiteboards.
CFU: Each student completes one of the two problems.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Have students work in pairs, and complete problems 5 & 6 on their
whiteboards.
CFU: Each student completes one of the two problems.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
CFU: Have students continue to work in pairs, but do their own work on a
separate sheet of paper. Complete the following three problems.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
What opportunities will students
have to read, write, listen &
Closure:
a. Students prove that they
know how to do the work
b. T. verifies that students can
describe the what and why
3
Students will be answering questions, writing notes and problems, describing
the process to the teacher and their peers, and reading problems.
Based on SSS and SAS theorems and AA postulate, and two given triangles.
Write how each of the rules proves triangles are similar?
Lesson Design
of the work
c. Have each student perform
behavior
Independent Practice:
a. Have students continue to
practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
Assign the following problems.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Resources: materials needed
to complete the lesson
4
Whiteboard, protractor, ruler, poster paper
```