4-1 Classifying Triangles SWBAT: Identify and classify triangles by angle measures and side measures. G.6.

Slides:

Advertisements

Similar presentations

Draw the following: 1. acute triangle 2.right triangle 3.obtuse triangle 4. acute, scalene triangle 5.obtuse, isosceles triangle 6. right, scalene.

Advertisements

Triangles. A triangle is a polygon with three sides.

DO NOW 1) X = 180 2) 55 + X = 180 3) X + 58 = 90 4) 31 + X = 90.

3-5 Parallel Lines and Triangles. Classification by Sides (NOT in the book!) Equilateral TriangleIsosceles Triangle Scalene Triangle 3 congruent sides2.

Blue – 2/23/2015 Gold – 2/24/ Name 2 pair of alternate interior angles  5 &  3 and  4 &  1 2. What is the sum of m  1 + m  2 + m  3? 180°

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 Standard 4C.

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

3.4 & 4.5 Triangles.

Triangles & Congruence Advanced Geometry Triangle Congruence Lesson 1.

Classifying Triangles Angle Measures of Triangles.

5-1 Classifying Triangles Today we will be learning how to classify triangles according to length of sides and measurement of the angles.

6-1: Congruent Figures, Classifying Triangles, and Related Theorems

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

Triangles Part 1 The sum of the angles in a triangle is always equal to: 180°

Triangle Fundamentals

Triangles: Angle Sum & Classifying Triangles Tutorial 12b.

3-3 Parallel Lines & the Triangle Angle Sum Theorem M11.B B Objectives: 1) To classify triangles and find the measures of their angles. 2) To.

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

Objectives: Classify triangles and find the measures of their angles Use the exterior angles of triangles.

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 A polygon with three sides and three angles. A triangle can be names by its’ side lengths and angles. – Side lengths: isosceles, equilateral,

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

Triangles : a three-sided polygon Polygon: a closed figure in a plane that is made of segments, called sides, that intersect only at their endpoints,

Perpendicular Lines, Parallel Lines and the Triangle Angle- Sum Theorem.

Find the value of x. 1. x + 2x + 3x = 180 6x = x + x + 40 = x + (x + 1) + 35 = x + 40 = 180 x = 70 3x + 36 = x = 48.

Classifying Triangles. Two Ways to Classify Triangles  By Their Sides  By Their Angles.

Warm Ups Classify each angle Classify each angle Solve Each Equation x= x+105= x + 58 = x = 90.

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

Triangles The sum of the measures of the angles of a triangle is 180 degrees. m A + m B + m C = 180 o A BC An angle formed by a side and an extension.

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.

How to classify triangles and find the measures of their angles. Chapter 3.4GeometryStandard/Goal: 2.2, 4.1.

Triangles and Their Angles Geometry – Section 4.1.

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

4.1 Triangle Angle Sum and Properties. How many degrees in a triangle? The sum of the angles in any triangle is exactly 180 degrees.

Applying Triangle Sum Properties

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

Lesson 4 – 1 Classifying Triangles

5-1 Classifying Triangles

Warm Up 5-1 Classify each angle as acute, obtuse, or right

Triangle Fundamentals

Geometry 4.1 Triangle and Angles.

Section 3-4 Angles of a Triangle.

Triangle Fundamentals

Triangle Fundamentals

Section 4.1 : Classifying Triangles

4.1 Triangles and Angles.

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

Triangle Fundamentals

Objectives -triangle names -remote interior -exterior

Add up all the sides Perimeter of Area of a Rectangle: ANY polygon:

Triangle Fundamentals

Triangle Fundamentals

Drill 1) x = 180, solve for x 2) How many degrees do the interior angles of a triangle add up to. 3) What type of triangle has an angle that.

Chapter 4: Triangles Classifying Triangles by sides:

3-3 Parallel Lines & the Triangle Angle Sum Theorem

4-1 Vocabulary Acute triangle Equiangular triangle Right triangle

Intro to Triangles.

Naming Triangles Triangles are named by using its vertices.

Brett Solberg – AHS – ’11-’12

4-1 Classifying Triangles

Bellwork Solve for the variable.

Presentation transcript:

4-1 Classifying Triangles SWBAT: Identify and classify triangles by angle measures and side measures. G.6

Classifying Triangles by Angles: Recall that a triangle is a three-sided polygon. Triangle ABC, written as ABC, has parts that are named using A,B and C. A B C The sides of ABC are AB, BC, and CA The vertices are points A,B and C. The angles are <BAC or <A, <ABC or <B and <BCA or <C Triangles can be classified in two ways-by their angles or by their sides. All triangles have at least two acute angles, but the third angle is used to classify the triangle.

Acute Triangle: 3 acute angles Equiangular Triangle: 3 congruent acute angles Obtuse Triangle: 1 obtuse angle Right Triangle: 1 right angle

Classify each triangle as acute, equiangular, obtuse, or right. 70o 40o 30o 60o 30o 120o 20o

Classify XYZ as acute, equiangular, obtuse, or right. Explain your reasoning 40o 50o 40o 50o X Y Z W

Classifying Triangles by Sides: Triangles can also be classified according to the number of congruent sides they have. To indicate that sides of a triangle are congruent, an equal number of hash marks is drawn on the corresponding sides. Equilateral Triangle: 3 congruent sides Isosceles Triangle: 2 congruent sides Scalene Triangle: no congruent sides

If point M is the midpoint of JL, classify JKM as equilateral, isosceles, or scalene. Explain your reasoning. 1.3 J K L M Now, classify KML as equilateral, isosceles or scalene.

Find the measures of the sides of isosceles triangle ABC. 9x-1 4x+1 5x-0.5 A B C Find the length of each side.

Find the measures of the sides of equilateral triangle FGH. Find the length of each side. 2y+5 3y-3 5y-19

4-2 Angles of Triangles

Triangle Angle-Sum Theorem: Gives us the relationship among the interior angle measures of any triangle. Triangle Angle-Sum Theorem Theorem 4.1 Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180.

Find the measures of each numbered angle. Find the Measures of Each Numbered Angle

Exterior Angle Theorem A triangle can have exterior angles formed by one side of the triangle and the extension of an adjacent side. Each exterior angle of a triangle has two remote interior angles that are not adjacent to the exterior angle. Ex. Theorem 4.2 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Example 3 Find Angle Measures in Right Triangles Find the measures of each numbered angle.