Chapter 4: Congruent Triangles

Slides:

Advertisements

Similar presentations

Report by Jennifer Johnson

Advertisements

2x 4y 10 2 x + 4y 2x + 4y = 102 x + 4y + 102= 180 2x = y 51 – 2y + 4y = 180 2y = 180 2y = 27 x = y x = 51 – 2(13.5) x = 51 – 27.

Triangles. A triangle is a polygon with three sides.

Classifying Triangles

 Classify each angle as acute, obtuse or right 90 o 72 o 116 o  How do we know that angle 1 and angle 2 are congruent? 1 2.

Applying Triangle Sum Properties

Triangles 1 The Basics. 2 Naming Triangles For example, we can call the following triangle: Triangles are named by using its vertices. ∆ABC∆BAC ∆CAB∆CBA∆BCA.

-Classify triangles and find measures of their angles.

Chapter 4 Congruent Triangles. 4.1 & 4.6 Triangles and Angles Triangle: a figure formed by three segments joining three noncollinear points. Classification.

Chapter 4 Congruent Triangles In this chapter, you will: classify triangles by their parts, apply the Angle Sum Theorem and the Exterior Angle Theorem,

Classifying Triangles & Angles of Triangles

4.1 Triangles and Angles Pg 194. Triangles Triangle-figure formed by 3 segments joining 3 noncollinear pts. Triangles are named by these three pts (ΔQRS)

Geometry. Kinds of triangles Geometry Kinds of triangles.

Classifying Triangles Angle Measures of Triangles.

4.1 – Apply Triangle Sum Properties

Triangles 11.2.

Chapter 4.1 Notes: Apply Triangle Sum Properties Goal: You will classify triangles and find measures of their angles.

Triangle Fundamentals

Angles of Triangles Chapter 4, Section 2. Angle Sum Theorem The sum of angles in a triangle is 180 o

Triangles and Angles Sec 4.1 GOALS: To classify triangles by their angles and sides To find missing angle measures in triangles.

Chapter 4.1 Notes: Apply Triangle Sum Properties

Section 3-4: Parallel Lines and the Triangle Angle-Sum Theorem.

4.1 & 4.2 A Notes. Type of ∆DefinitionPicture Equilateral Triangle CLASSIFICATION BY SIDES All sides are 

Triangles Geometry Mr. Zampetti Unit 3, Day 1. Today’s Objectives To learn new strategies that will help find the measures of angles in a triangle To.

Triangle Classification. Objectives Classify triangles by their angle and side measures Find the sum of the measure of the interior and exterior angles.

Classify triangles by sides No congruent sides Scalene triangle At least two sides congruent Isosceles triangle Three congruent sides Equilateral triangle.

Goal, to classify triangles by their sides and by their angles.

4-1 Triangles and Angles. Theorem 4.1: Triangle Sum The sum of the measures of the interior angles of a triangle is 180 . xx yy zz  x +

Lesson: Objectives: 4.1 Classifying Triangles  To IDENTIFY parts of triangles  To CLASSIFY Triangles by their Parts.

4.1 & 4.2 A Notes. Type of ∆DefinitionPicture Equilateral Triangle CLASSIFICATION BY SIDES All sides are 

4.1 Triangles and Angles. 2 Standard/Objectives: Objectives: Classify triangles by their sides and angles. Find angle measures in triangles DEFINITION:

Section 3.3 Triangles Thompson. Triangle Sum Theorem The sum of the measures --?--.

Geometry Section 4.1 Triangle Sum Theorem. A triangle is the figure formed by three line segments joining three noncollinear points. A B C.

4.1 Classifying Triangles textbook page 173 Classification by Sides  Equilateral – 3 congruent sides  Isosceles – 2 congruent sides  Scalene – no.

Applying Parallel Lines to Polygons Lesson 3.4 Pre-AP Geometry.

3.4.  The sum of the measures of the angles of a triangle is 180.

Section 3-4 Angles of Triangles What is a triangle?

Triangles Chapter What is the sum of the angles inside a triangle? 180º? Prove it m Given A B C Angle Addition Postulate/Definition of a Straight.

Triangles and Their Angles Geometry – Section 4.1.

3-4 Angles of a Triangle. A Triangle is a figure formed by three segments joining three noncollinear points. 1) Classifying triangles by their sides.

Classify These Triangles by Sides and Angles. Chapter 4 Congruent Triangles Section 4.1: Triangle Sum Properties Todays Objective: Determine if a right.

Geometry Section 4.1 Apply Triangle Sum Properties.

Applying Triangle Sum Properties

 Scalene Triangle No sides congruent  Isosceles Triangle Exactly 2 sides congruent  Equilateral Triangle All sides congruent.

Do Now Classify the following triangles as acute, right, or obtuse. 2.

4.1 Apply Triangle Sum Properties

Chapter 4: Congruent Triangles

Geometry 4.1 Triangle and Angles.

Bellwork Classify each angle as acute, obtuse, or right. 90° 72° 116°

Section 3-4 Angles of a Triangle.

Types of Triangles and Their Properties

Warm-Up And speaking of the final frontier, what do you think is the shape of space?

Chapter 4 Section 4.1 – Part 1 Triangles and Angles.

4.1 Triangles and Angles.

Lesson 3: Parallel Lines and the Triangle Angle-Sum Theorem

Objectives -triangle names -remote interior -exterior

4.1 Classifying Triangles

Unit 4 – Lesson 1 Apply Triangle Sum Properties

Triangles and Angles Section 4.1 and 4.2.

Lesson 5-1 Angles of Triangles.

Triangle Fundamentals

Chapter 4: Triangles Classifying Triangles by sides:

3-3 Parallel Lines & the Triangle Angle Sum Theorem

Classifying Triangles

4.1 – Apply triangle sum properties

4.1 Apply Triangle Sum Properties

Geometry 3.4 Angles of a Triangle.

Lesson 4-R Chapter 4 Review.

Presentation transcript:

Chapter 4: Congruent Triangles Section 4.1: Apply Triangle Sum Properties

Section 4.1: Apply Triangle Sum Properties A triangle with vertices A, B, and C is called “triangle ABC” or “Δ ABC” A vertex of a triangle is a point that joins two sides of a triangle. The side across from an angle is the opposite side. A c b B C a

Section 4.1: Apply Triangle Sum Properties Triangle Classifications: A triangle can be identified by its sides and by its angles Classifications by sides: (Draw the triangles accurately using rulers!) Scalene: no sides are equal Isosceles: 2 sides are equal Equilateral: 3 sides are equal Note: an equilateral triangle is also equiangular (all angles are equal)

Section 4.1: Apply Triangle Sum Properties Triangle Classifications by Angles: Acute: all 3 angles are acute Right: has one right angle Obtuse: has one obtuse angle

Identify each triangle by its sides and by its angles Isosceles, Acute 1) 2) 3) 4) 5) Isosceles, Right Scalene, Obtuse Scalene, Right Equilateral, Equiangular or Acute

Section 4.1: Apply Triangle Sum Properties Triangle Sum Theorem: The sum of the interior angles in a triangle is 180º Examples: Find the value of x: 50º 20º xº

Section 4.1: Apply Triangle Sum Properties 2) Find the value of x and the angle measurements: (x + 16)º (2x)º xº

Section 4.1: Apply Triangle Sum Properties A corollary to a theorem is a statement that can be proved using the theorem. Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary.

Section 4.1: Apply Triangle Sum Properties Interior Angles: Angles inside a triangle (or any polygon) Exterior Angles: Angles that form linear pairs with the interior angles.

Section 4.1: Apply Triangle Sum Properties Exterior Angle Theorem: If one side of a triangle is extended, then the angle formed is equal to the sum of the two remote interior angles 150º 65º 85º Exterior angle Remote interior Remote Interior

Section 4.1: Apply Triangle Sum Properties Find the value of x: 7) Find the value of x and the angle measurements: (x + 4)º (2x – 1)º (6x)º (3x + 15)º (2x – 9)º (2x + 3)º

Section 4.1: Apply Triangle Sum Properties Homework: Pg. 221 #1-10 (all), #14-20 (all)