Kickoff 7.1.1 Exploration
Performance Based Objective: Students will be able to identify and apply the properties of similar polygons in order to solve problems.
Agenda | Time |
Kickoff | 20 min |
Return | 20 min |
10 min | |
2 Minute Warning Self-Assessment | 5 min |
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Identify and apply properties of similar polygons to solve problems.
Objectives
similar
similar polygons
similarity ratio
Vocabulary
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.
Figures that are similar (~) have the same shape but not necessarily the same size.
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Example 1: Describing Similar Polygons
Match the pairs of congruent angles and corresponding proportional sides.
Nearpod matching activity
0.5
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
A similarity ratio is the ratio of the lengths of
the corresponding sides of two similar polygons.
The similarity ratio of ∆ABC to ∆DEF is , or .
The similarity ratio of ∆DEF to ∆ABC is , or 2.
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.
Writing Math
When you work with proportions, be sure the ratios compare corresponding measures.
Helpful Hint
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Example 2B: Identifying Similar Polygons
Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.
∆ABCD and ∆EFGH
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Example 3: Hobby Application
Find the length of the model to the nearest tenth of a centimeter.
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Kickoff 7.1.2
Today’s Goals: Identify and apply properties of similar polygons to solve problems.
Agenda | Time |
Kickoff | 15 min |
Return | 30 min |
5 min | |
2 Minute Warning Self-Assessment | 5 min |
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
7.1.1 Recap
Today’s Goals: Identify and apply properties of similar polygons to solve problems.
What were the main takeaways from the previous class (7.1.1)?
Rewrite this sentence with your thoughts: Yesterday I thought ..... but after lesson 7.1.1, I realized .....
What two relationships arise when two polygons are similar?
Are ALL isosceles triangles similar? Why or why not?
Are ALL regular polygons similar? Why or why not?
If two shapes are similar, how would you find the value of a missing side length/distance?
Agenda | Time |
Kickoff | 20 min |
Return | 20 min |
10 min | |
2 Minute Warning Self-Assessment | 5 min |
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Lesson Quiz: Part I
1. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.
2. The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is . If the length of the model is 10 inches, what is the length of the actual sailboat in feet?
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Lesson Quiz: Part II
3. Tell whether the following statement is sometimes, always, or never true. Two equilateral triangles are similar.
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
Kickoff 7.1.2
Solve each proportion.
1. 2.
3. A diagram of a new competition swimming
pool is shown. If the width of the actual pool
is 30 meters, find the length of the actual
pool.
Today’s Goals: Identify and apply properties of similar polygons to solve problems.
Agenda | Time |
Kickoff Exploration 7.1.2 | 10 min |
Return | 20 min |
15 min | |
2 Minute Warning Self-Assessment | 5 min |
Holt McDougal Geometry
7-1
Ratios in Similar Polygons
1. Copy △ABC on a piece of graph paper.
2. Draw another △DEF that has the same
shape as △ABC but is a different size.
3. Explain how you know that △DEF has
the same shape as △ABC.
4. Use a protractor to measure the angles of △ABC and △DEF. What do you notice?
5. How do the side lengths of △ABC and △DEF compare?
6. Complete the following conjecture: Two polygons are similar polygons if and only if their corresponding angles are ………… and their corresponding sides are …………
7. Discuss whether the two rectangles
are similar. Explain why or why not.
8. Explain why two congruent triangles
are also similar to each other.
Today’s Goals: Identify and apply properties of similar polygons to solve problems.
Agenda | Time |
Kickoff | 20 min |
Return | 25 min |
5 min | |
2 Minute Warning Self-Assessment | 5 min |
Holt McDougal Geometry
7-1
Ratios in Similar Polygons