# Similarity and Congruence

Philosophy of Mathematics |

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# Concept Map

# Textbook

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# Additional Information

## Useful websites

## Reference Books

# Teaching Outlines

## Concept #1 - Understanding similarity

### Learning objectives

- To show similar planar figures, discuss congruence and properties of congruent/ similar triangles

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activity No #1 Identifying similar shapes, similar triangles

**Estimated Time**- 80 minutes (40 +40)**Materials/ Resources needed**- Blackboard, Geogebra files + projector, Calculator**Prerequisites/Instructions, if any****Multimedia resources**

Suchetha . S. S Asst. Teacher ( Mathematics ) GJC Thyamagondlu. Nelamangala Talluk Bangalore Rural District doing the activity below on a lesson on similar triangles using GeoGebra in the classroom

**Website interactives/ links/ Geogebra Applets****Process (How to do the activity)**

- Draw figures on the boards - planar figures and triangles
- Draw pairs of figures on the board [ both similar and dissimilar]; they can identify overlap of congruent figures
- Demonstrate using Geogebra files and discuss
- As part of the procedure, the teacher can use the following points to evaluate the activity as well as evaluate student understanding

- Confusion between congruence and similarity
- When they give the theorem, if they cannot identify included side and angle
- When there is a wrong answer, identify what is the source of the confusion – sides, ratio and proportion
**Developmental Questions (What discussion questions)**

- Can you identify similar figures?
- If the children know the names of the theorem, can they explain SSS, AAA, ASA?
- What does a ratio of side mean? What is proportionality?
- In the Geogebra files, when I change the sides/ proportion, the triangles change in size. But the proportion remains the same, angle remains the same
- With calculator verify the proportion (this is very very useful for involving the whole class) they all can see the proportion remains constant though the size changes
- Show the arithmetic behind the proportion

**Evaluation**

- Direct substitution in simple textbook problems
- With a pencil and a ruler, how can you estimate the height of a pole

**Question Corner**

### Activity No # 2 Review of the concepts of similarity and congruence

**Estimated Time**- 30 minutes**Materials/ Resources needed**-Projector, Computer**Prerequisites/Instructions, if any****Multimedia resources**

**Website interactives/ links/ Geogebra Applets****Process (How to do the activity)****Developmental Questions (What discussion questions)****Evaluation (Questions for assessment of the child)****Question Corner**

## Concept #

### Learning objectives

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activity No #

**Estimated Time****Materials/ Resources needed****Prerequisites/Instructions, if any****Multimedia resources****Website interactives/ links/ Geogebra Applets****Process (How to do the activity)****Developmental Questions (What discussion questions)****Evaluation (Questions for assessment of the child)****Question Corner**

### Activity No #

**Estimated Time****Materials/ Resources needed****Prerequisites/Instructions, if any****Multimedia resources****Website interactives/ links/ Geogebra Applets****Process (How to do the activity)****Developmental Questions (What discussion questions)****Evaluation (Questions for assessment of the child)****Question Corner**

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