# Chapter 5 - PowerPoint PPT Presentation

1 / 27

Chapter 5. Triangles and Congruence. Section 5-1. Classifying Triangles. Triangle. A figure formed when three noncollinear points are joined by segments. Triangles Classified by Angles. Acute Triangle – all acute angles Obtuse Triangle – one obtuse angle

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

### Download Presentation

Chapter 5

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## Chapter 5

Triangles and Congruence

### Section 5-1

Classifying Triangles

### Triangle

• A figure formed when three noncollinear points are joined by segments

### Triangles Classified by Angles

• Acute Triangle – all acute angles

• Obtuse Triangle – one obtuse angle

• Right Triangle – one right angle

### Triangles Classified by Sides

• Scalene Triangle – no sides congruent

• Isosceles Triangle– at least two sides congruent

• Equilateral Triangle – all sides congruent (also called equiangular)

### Section 5-2

Angles of a Triangle

### Angle Sum Theorem

• The sum of the measures of the angles of a triangle is 180.

### Theorem 5-2

• The acute angles of a right triangle are complementary.

### Theorem 5-3

• The measure of each angle of an equiangular triangle is 60.

### Section 5-3

Geometry in Motion

### Translation

• When you slide a figure from one position to another without turning it.

• Translations are sometimes called slides.

### Reflection

• When you flip a figure over a line.

• The figures are mirror images of each other.

• Reflections are sometimes called flips.

### Rotation

• When you turn the figure around a fixed point.

• Rotations are sometimes called turns.

### Pre-image and Image

• Each point on the original figure is called a pre-image.

• Its matching point on the corresponding figure is called its image.

### Mapping

• Each point on the pre-image can be paired with exactly one point on the image, and each point on the image can be paired with exactly one point on the pre-image.

### Section 5-4

Congruent Triangles

### Congruent Triangles

• If the corresponding parts of two triangles are congruent, then the two triangles are congruent

### Corresponding Parts

• The parts of the congruent triangles that “match”

### Congruence Statement

• Δ ABC ≅Δ FDE

• The order of the vertices indicates the corresponding parts

### CPCTC

• If two triangles are congruent, then the corresponding parts of the two triangles are congruent

• CPCTC – corresponding parts of congruent triangles are congruent

SSS and SAS

### Postulate 5-1

• If three sides of one triangle are congruent to three corresponding sides of another triangle, then the triangles are congruent. (SSS)

### Included Angle

• The angle formed by two given sides is called the included angle of the sides

### Postulate 5-2

• If two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. (SAS)

ASA and AAS

### Postulate 5-3

• If two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent.

### Theorem 5-4

• If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and nonincluded side of another triangle, then the triangles are congruent.