Similarities : Solving Problems: Congruence, Similarity, Trigono

Unit 2- Similarities

​Solving Problems: Congruence, Similarity, Trigonometry, and Pythagorean Theorem

Introduction:Congruence, Similarity, Pythagorean Theorem, and Trigonometry

The lesson covers Congruence, Similarity, the Pythagorean Theorem, and Trigonometry, essential concepts in geometry that help understand relationships between shapes, angles, and measurements. Congruence involves identifying identical shapes regardless of their position, while Similarity focuses on figures of the same shape but different sizes, maintaining proportions. The Pythagorean Theorem is crucial for calculating the length of a side in right triangles when the other two sides are known. Trigonometry deals with sine, cosine, and tangent, key for relating angles and sides of right triangles, useful in various fields. The lesson includes activities to enhance problem-solving skills and understanding of these principles.

• Solving problems with triangle congruence

• Use trigonometric ratios to solve right triangle

• Use similarity to solve geometric problems

• Find the Missing sides of right triangles

​By the end of this lesson, students will:

Learning Objectives

Learning Objectives​

In this lesson, we will begin by exploring Congruence, a fundamental concept in geometry. Congruence helps us understand how to determine if two shapes are identical in size and shape.

When two figures are congruent, they can be perfectly aligned, no matter how they are rotated, flipped, or shifted.

This concept is crucial for identifying identical geometric figures and plays a vital role in various fields, from architecture to design. Let's dive in and learn how to recognize and prove the congruence of shapes!

​Congruence

Open Ended

The previous slide, suggested that congruence is evidenced in various fields, from architecture to design. Do a google search to find other real world applications of Congruence,

Open Ended

In your own words, explain what is congruence, and give an example.

Main Take-A-Way

​Congruence

​Criteria

​Same Shape and Same Size

​Congruence Means:

​1.SSS,

2.SAS,

3.ASA,

4.AAS,

5.HL

Draw

Draw a diagram that you can use to remember the four criteria for congruence.

Multiple Choice

Which of the following is NOT a condition for congruence?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

• Side-Side-Angle (SSA)

Drag and Drop

Complete the following criteria for congruence



Side, Side, ​

Placeholder

Drag these tiles and drop them in the correct blank above

Side

Angle

Drag and Drop

Complete the following criteria for congruence



Side,​

Placeholder

Side

Drag these tiles and drop them in the correct blank above

Side

Angle

Drag and Drop

Complete the following criteria for congruence

Angle,

Placeholder

, Side

Drag these tiles and drop them in the correct blank above

Side

Angle

Drag and Drop

Complete the following criteria for congruence

Angle,

Placeholder

, Angle

Drag these tiles and drop them in the correct blank above

Side

Angle

​Congruence

Lisson carefully as you will beask to list two things to learned from this video.

Discussion Activity
(Group )

Multiple Choice

Using the congruency statement, which angle must be congruent to the below angle?

$$\angle H\cong?$$  

• $$\angle E$$  

• $$\angle F$$

• $$\angle I$$  

• not congruent to another angle

Multiple Choice

Are these triangles congruent by SSS?

• Yes

• NO

Multiple Choice

Are these triangles congruent by SSS?

• Yes

• No

Multiple Choice

Are the 2 triangles congruent by SSS and give a congruence statement

• Yes $$\Delta ADB\ \cong\Delta CDB$$

• Yes $$\Delta ADB\ \cong\Delta CBD$$

• No

• Yes $$\Delta BAD\cong\Delta BDC$$

Multiple Choice

Are the triangles shown congruent by SAS?

• yes

• no

Multiple Choice

Which property is used to show the following:

$$\overline{AD}\cong\overline{AD}$$  

• Symmetric 

• Reflexive

• Inverse

• Identity

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• AAS
• SSS
• SAS
• SSA

Multiple Choice

State if the two triangles are congruent. If they are, state how you know

• AAS
• ASA
• Not congruent

Multiple Choice

State if the two triangles are congruent. If they are, state how you know

• AAS
• ASA
• Not congruent