Congruence and Similarity

Slides:

Advertisements

Similar presentations

1B_Ch11(1). 11.1The Meaning of Congruence A Congruent Figures B Transformation and Congruence C Congruent Triangles Index 1B_Ch11(2)

Advertisements

Similar and Congruent Figures. Similar figures have the same shape, but not the same size. They must have the same ratio of side lengths Congruent figures.

Congruent and Similar. Similar and Congruent Figures Congruent polygons have all sides congruent and all angles congruent. Similar polygons have the same.

Students will be able to: identify the 4 triangle similarity tests to solve problems involving congruency.

Form 1 Mathematics Chapter 11.  Lesson requirement  Textbook 1B  Workbook 1B  Notebook  Before lessons start  Desks in good order!  No rubbish.

9-7:Congruent and Similar Figures Congruent Figures Similar Figures.

Connection to previews lesson… Previously, we studied rigid transformations, in which the image and preimage of a figure are congruent. In this lesson,

Math 10 Ms. Albarico. A.Modeling Situations Involving Right Triangles B.Congruence and Similarity 5.1 Ratios Based on Right Triangles.

INTRODUCTION TO COORDINATES Form 1 Mathematics Chapter 8.

Introduction to Statistics

7-5 Congruent Figures Warm Up

11.5 Similar Triangles Identifying Corresponding Sides of Similar Triangles By: Shaunta Gibson.

Dilations Shape and Space. 6.7 cm 5.8 cm ? ? Find the missing lengths The second picture is an enlargement of the first picture. What are the missing.

Congruence If shapes are identical in shape and size then we say they are congruent. Congruent shapes can be mapped onto each other using translations,

Figures & Transformations By: Ms. Williams. Congruent Figures 1. Name 2 corresponding sides and 2 corresponding angles of the figure. y.

1 Press Ctrl-A ©G Dear 2009 – Not to be sold/Free to use Similar Triangles Stage 6 - Year 11 General Mathematics Preliminary.

Form 1 Mathematics Chapter 9. Lesson requirement Textbook 1B Workbook 1B Notebook Folder Before lessons start Desks in good order! No rubbish around!

Form 1 Mathematics Chapter 5.  Lesson requirement  Textbook 1A  Workbook 1A  Notebook (and folder)  Before lessons start  Desks in good order! 

Form 1 Mathematics Chapter 12.  Lesson requirement  Textbook 1B  Workbook 1B  Notebook  Before lessons start  Desks in good order!  No rubbish.

Congruence and Similarity

Form 1 Mathematics Chapter 12.  Lesson requirement  Textbook 1B  Workbook 1B  Notebook  Before lessons start  Desks in good order!  No rubbish.

Form 1 Mathematics Chapter 10.  Lesson requirement  Textbook 1B  Workbook 1B  Notebook  Before lessons start  Desks in good order!  No rubbish.

Dilations Advanced Geometry Similarity Lesson 1A.

Form 1 Mathematics Chapter 11.  Lesson requirement  Textbook 1B  Workbook 1B  Notebook  Before lessons start  Desks in good order!  No rubbish.

Chapter 4.2 Notes: Apply Congruence and Triangles

Form 1 Mathematics Chapter 9. Lesson requirement Textbook 1B Workbook 1B Notebook Folder Before lessons start Desks in good order! No rubbish around!

 A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new figure is called the image. Another.

Form 1 Mathematics Chapter 6.  Lesson requirement  Textbook 1A  Workbook 1A  Notebook  Folder  Before lessons start  Desks in good order!  No.

Form 1 Mathematics Chapter 6.  Lesson requirement  Textbook 1A  Workbook 1A  Notebook (and folder)  Before lessons start  Desks in good order! 

Chapter13-6 Similar and Congruent Figures

Lesson 4-3 Congruent Triangles.

Things Needed Today (TNT): Topic: Congruency & Review of Rotations

Transformations What’s it all about?.

Bell Work: Solve the proportion 9 = 18 3 d

Geometry: Wednesday March 28th

Connection to previews lesson…

Module 11 So Far… Dilation is a transformation that makes an image that is the same shape, but may be a different size “Length” could be side length or.

DO NOW Directions (Part 1):

Do Now: 1) x = 8 2) x = 14 3) x = 6, –6 4) x = 9, –6.

Similar figures are figures that have the same shape but not necessarily the same size. The symbol ~ means “is similar to.” 1.

Congruence and Similarity pg. 87

Area and Volume Form 1 Mathematics Chapter 7.

Angles in Intersecting and Parallel Lines

Similar Polygons.

Angles in Intersecting and Parallel Lines

Congruence “Same size, same shape”

Chapter 4.2 Notes: Apply Congruence and Triangles

TRIGONOMETRY Math 10 Ms. Albarico.

Turn to Page S.35.

Congruence and Similarity

Estimation in numbers and measurement

Make your new weekly Warm up Page

Day 52 – Identifying congruent angles of a triangle

INTRODUCTION TO COORDINATES

Make your new weekly Warm up Page

Introduction to Geometry

Introduction to Statistics

Congruence Transformations

Congruence Lesson 9-5.

Chapter 7 Isometry & similitude.

SIMILARITY AND CONGRUENCY

Transformations.

Congruent and Similar Shapes

Similar and Congruent Figures. Similar figures have the same shape, but not the same size. They must have the same ratio of side lengths Congruent figures.

Presentation transcript:

Congruence and Similarity Form 1 Mathematics Chapter 11

Reminder Lesson requirement Before lessons start Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish around! No toilets! Keep your folder at home Prepare for Final Exam

Reminder Missing HW SHW (I) SHW (II) OBQ CBQ Detention 8th May (Wednesday) SHW (II) 14th May (Tuesday) OBQ 15th May (Wednesday) CBQ 20th May (Monday)

Congruence (全等, p.172) Congruent figures (全等圖形) 1. Figures having the same shape and size are called congruent figures. e.g. Figures X and Y below are congruent figures. X Y 2. Two congruent figures can fit exactly on each other.

Time for Practice Page 173 of Textbook 1B Class Practice Pages 176 – 177 of Textbook 1B Questions 1 – 2 Page 73 of Workbook 1B Question 1

Transformation and Congruence (p.174) We learnt transformations in Chapter 9: Translation Reflection Rotation Enlargement and Reduction Which one will NOT change the shape? Try Class Discussion on p.174

Transformation and Congruence (p.174) 1. When a figure is translated, rotated or reflected, the image produced is congruent to the original figure. 2. When a figure is reduced or enlarged, the image produced will not be congruent to the original one.

Congruent Triangles (全等三角形, p.175) Symbol “  ” means “is congruent to” When two triangles are congruent, (i) their corresponding sides (對應邊) are equal, (ii) their corresponding angles (對應角) are equal. e.g. If △ABC  △XYZ, then AB = XY, BC = YZ, CA = ZX, A = X, B = Y, C = Z. A B C X Y Z

Congruent Triangles (p.175) Example 1: Name a pair of congruent triangles in the figure. From the figure above, we have △ABC  △RQP.

Congruent Triangles (p.175) Example 2: Given that △ABC  △XYZ, find the unknowns x, b and y. ∵ The corresponding sides and corresponding angles of two congruent triangles are equal, ∴ x = 5 cm, b = 6 cm, y = 50°

Congruent Triangles (p.175) Example 3: Given that △PQS  △RSQ, find the unknowns s and r. Since △PQS  △RSQ, we have PQ = RS i.e. s = 8 cm and RQS = PSQ = 70° In △RSQ, 45° + RQS + r = 180° 45° + 70° + r = 180° 115° + r = 180° r = 65°

Time for Practice Page 176 of Textbook 1B Class Practice Pages 177 – 178 of Textbook 1B Questions 4 – 17 Pages 74 – 75 of Workbook 1B Questions 2 – 5

Enjoy the world of Mathematics! Ronald HUI