4.2: Measuring Angles in Triangles

Slides:

Advertisements

Similar presentations

Warm Up Determine the measure of the missing interior angle. What type of triangle is it? Unit 8 - Lesson 2 Exterior Angles of a Triangle.

Advertisements

Lesson 3-4 (Parallel & Perpendicular Lines) perpendicula r parallel.

4.2 Angles of Triangles.

Classifying Triangles

4.2 Angles of Triangles Objectives: *Apply the Angle Sum Theorem.

 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

HOW TO FIND AN ANGLE MEASURE FOR A TRIANGLE WITH AN EXTENDED SIDE

 Grab a red pen and have your homework out ready to grade.

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)

Classifying Triangles Angle Measures of Triangles.

4.1 – Apply Triangle Sum Properties

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

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

3.4 parallel Lines and the Triangle Angle-Sum Theorem

Wednesday, Oct. 3, 2012 No Mental Math. No TISK. Discuss Marvelous Shot problem. HW: p. 193 #14-19,

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

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.

Warm-Up Exercises 1.90º 2. 72º Classify each angle as acute, obtuse, or right º 4. How do you know that 1 = 2? ~ 2 1.

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 +

Triangle Angle Sum Theorem, Triangle Exterior Angle Theorem

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 

Triangle Sum Properties

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

Geometry Triangles. Vocabulary  Theorem 4-1 (angle sum theorem): The sum of the measures of the angles of a triangle is 180 In order to prove the angle.

 4.1 Classifying Triangles. Example 1 Example 2.

3.5 Parallel Lines and Triangles

Angles of Triangles Angle Sum Theorem The sum of the measures of the angles of a triangle is 180 degrees. Third Angle Theorem If two angles of one triangle.

HONORS GEOMETRY 4.2. Angles of Triangles. Do Now: Classify the following triangles and then find x and ?.

3-4: Angles of a Triangle. A triangle is the figure formed by 3 segments joining 3 noncollinear points. The points are called vertices (plural of.

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

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.

Geometry Section 4.1 Apply Triangle Sum Properties.

Applying Triangle Sum Properties

CH. 4.1 APPLY TRIANGLE SUM PROPERTIES. VOCAB Interior Angles : angles inside the triangle (sum = 180) Exterior Angles: angles outside the triangle Interior.

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

Angles of Triangles.

Section 4-1 Triangles and Angles.

Chapter 4: Congruent Triangles

Name the type of triangle shown below.

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

Angles of Triangles 4.2.

Exterior Angles of Triangles

Notecards Unit 4 Triangle Properties.

Section 3-4 Angles of a Triangle.

A C B Triangle Sum Theorem (4.1)

Chapter 4: Congruent Triangles

4.2 Angles of Triangles Theorem 4-1: Angle Sum Theorem

4.1 Triangles and Angles.

Warm-up Find x a) b).

Objectives -triangle names -remote interior -exterior

Exterior Angles of Triangles

Warm-up Find x a) b).

Unit 4 – Lesson 1 Apply Triangle Sum Properties

Triangles and Angles Section 4.1 and 4.2.

Warm-up Find x a) b).

V L T The sum of the interior angles of a triangle is 180 degrees.

Base Angles & Exterior Angles

Isosceles Triangles. Isosceles Triangles Base Angles If 2 angles in a triangle are congruent, then the sides opposite them are congruent.

Isosceles Triangles. Isosceles Triangles Base Angles If 2 angles in a triangle are congruent, then the sides opposite them are congruent.

Exterior Angle Theorem

Classifying Triangles

4.1 – Apply triangle sum properties

Triangles and Angles.

Presentation transcript:

4.2: Measuring Angles in Triangles p. 189-195

Thm 4.1:Triangle Sum Thm A B C The sum of the measures of the interior angles of a triangle is 180o. mA + mB+ mC=180o + + = 180 A B C

Example 1 Name Triangle AWE by its angles mA + mW+ mE=180o (3x+5) + ( 8x+22) + (4x-12) = 180 A 15x + 15 = 180 15x = 165 x = 11 3x +5 mA = 3(11) +5 = 38o 8x + 22 mW = 8(11)+22 = 110o 4x - 12 W mE = 4(11)-12 = 32o E Triangle AWE is obtuse

Example 2 Solve for x . Ans: (5x+24) + (5x+24) + (4x+6) = 180

Exterior Angles (formed by extending the sides) )) ((

Thm 4.2: Exterior Angles Thm The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. m1=mA+ mB m1= + A 1 B C

Example Find every angle measure Exterior angle = 2 nonadjacent angles 65 3x-10 = (25) + (x+15) 3x-10 = x +40 2x= 50 x = 25 115 40

Exterior angle example Solve for q

Example Find the missing angles 80 80 60 40 50 50 70 110 110 70

Find the measure of each numbered angle in the figure. Example Find the measure of each numbered angle in the figure.

Corollary to triangle sum thm (Corollary- a statement easily proved using a thm.) * The acute angles of a right triangle are complementary. A A is comp. to C B C