Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The...

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Lesson 5-3 Inequalities in one Triangle

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Transcript of Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The...

Page 1: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Lesson 5-3 Inequalities in one

Triangle

Page 2: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

VocabularyTheorem 5.8: Exterior Angle InequalityThe measure of an exterior angle of a

triangle is greater than the measure of either of its corresponding remote interior angles.

Page 3: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 1

A.B.C.D.

Page 4: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 1

A.B.C.D.

Page 5: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

VocabularyTheorem 5.9: Angle-Side Relationship #1If one side of a triangle is longer than

another side, then the angle opposite the longer side has a greater measure than the side opposite the shorter side.

Page 6: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

VocabularyTheorem 5.10: Angle-Side Relationship #2If one angle of a triangle has greater

measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

Page 7: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 2Order Triangle Angle Measures

List the angles of ΔABC in order from smallest to largest.

Answer: C, A, B

Page 8: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 2

A. X, T, V

B. X, V, T

C. V, T, X

D. T, V, X

List the angles of ΔTVX in order from smallest to largest.

Page 9: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 3Order Triangle Side Lengths

List the sides of ΔABC in order from shortest to longest.

Answer: AC, AB, BC

The angles from smallest to largest are B, C, and A. The sides opposite these angles are AC, AB, and BC, respectively. So, the sides from shortest to longest are AC, AB, BC.

Page 10: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 3List the sides of ΔRST in order from shortest to longest.

A. RS, RT, ST

B. RT, RS, ST

C. ST, RS, RT

D. RS, ST, RT

Page 11: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 4Angle-Side Relationships

HAIR ACCESSORIES Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions tell her to tie the two smaller angles of the triangle under her hair. If she folds the handkerchief with the dimensions shown, which two ends should she tie?

Answer: So, Ebony should tie the ends marked Y and Z.

Page 12: Lesson 5-3 Inequalities in one Triangle. Vocabulary Theorem 5.8: Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than.

Example 4

A. A and DB. B and FC. C and ED. A and B

KITE ASSEMBLY Tanya is following directions for making a kite. She has two congruent triangular pieces of fabric that need to be sewn together along their longest side. The directions say to begin sewing the two pieces of fabric together at their smallest angles. At which two angles should she begin sewing?


SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

SWBAT… … find the measures of angles of triangles using the Triangle Sum Theorem and Triangle Exterior Angle Theorem Agenda 1. Warm-up (10 min) 2. Review.

4.1 Apply Triangle Sum Properties - Denton ISD Apply Triangle Sum Properties ... Exterior Angle Theorem ... 6. 7. 7. EXAMPLE 4 Choose a postulate or theorem Gate ...

4.1 Apply Triangle Sum Properties - Denton ISD Apply Triangle Sum Properties ... Exterior Angle Theorem ... 6. 7. 7. EXAMPLE 4 Choose a postulate or theorem Gate ...

All Triangles= 180 degrees. Right Triangle One angle is 90 (a right angle) Right Triangle One angle is 90 (a right angle) Scalene No sides or angles.

All Triangles= 180 degrees. Right Triangle One angle is 90 (a right angle) Right Triangle One angle is 90 (a right angle) Scalene No sides or angles.

Unit 3 Triangles. Chapter Objectives Classification of Triangles by Sides Classification of Triangles by Angles Exterior Angle Theorem Triangle Sum Theorem.

Unit 3 Triangles. Chapter Objectives Classification of Triangles by Sides Classification of Triangles by Angles Exterior Angle Theorem Triangle Sum Theorem.

5.5 Inequalities in Triangles - Typepad · 5.5 Inequalities in Triangles Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater

5.5 Inequalities in Triangles - Typepad · 5.5 Inequalities in Triangles Corollary to the Triangle Exterior Angle Theorem: The measure of an exterior angle of a triangle is greater

Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Geometry Lesson 4 – 2 Angles of Triangles Objective: Apply the triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem.

Polygon Exterior Angle Sum.pdf

Polygon Exterior Angle Sum.pdf

Chapter 4 Congruent Triangles. Chapter Objectives Classification of Triangles by Sides Classification of Triangles by Angles Exterior Angle Theorem Triangle.

Chapter 4 Congruent Triangles. Chapter Objectives Classification of Triangles by Sides Classification of Triangles by Angles Exterior Angle Theorem Triangle.

Polygons - The Math Plane€¦ · Polygons Interior and Exterior Angle measures interior angle exterior angle Regular Hexagon Finding the sum of the exterior angles: 360 degrees in

Polygons - The Math Plane€¦ · Polygons Interior and Exterior Angle measures interior angle exterior angle Regular Hexagon Finding the sum of the exterior angles: 360 degrees in

Geometry - whsd.k12.pa.us 4... · the interiors of the the triangle. three angles. three angles of the triangle. CONJECTURE: Sum of the angles of any triangle is _____ Exterior Angle

Geometry - whsd.k12.pa.us 4... · the interiors of the the triangle. three angles. three angles of the triangle. CONJECTURE: Sum of the angles of any triangle is _____ Exterior Angle

Triangle Angle Sum Theorem Isosceles Triangles Equilateral Triangle.

Triangle Angle Sum Theorem Isosceles Triangles Equilateral Triangle.

§ 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem.

§ 7.1 Segments, Angles, and Inequalities § 7.4 Triangle Inequality Theorem § 7.3 Inequalities Within a Triangle § 7.2 Exterior Angle Theorem.

Skills Practice for Lesson 4 - Ms. Hollingsworth - HomeCh...exterior angle of a triangle is greater than the measure of either of the remote interior angles of the triangle. 2. The

Skills Practice for Lesson 4 - Ms. Hollingsworth - HomeCh...exterior angle of a triangle is greater than the measure of either of the remote interior angles of the triangle. 2. The

interior angles mZ4 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Third Angles Theorem If

interior angles mZ4 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Third Angles Theorem If

Triangles and their properties Triangle Angle sum Theorem External Angle property Inequalities within a triangle Triangle inequality theorem Medians Altitude.

Triangles and their properties Triangle Angle sum Theorem External Angle property Inequalities within a triangle Triangle inequality theorem Medians Altitude.

librarykvnewcanttblog.files.wordpress.com · Web viewIf an exterior angle of a triangle is 1300 and one of the interior opposite angle is 600. Find the other interior opposite angle.

librarykvnewcanttblog.files.wordpress.com · Web viewIf an exterior angle of a triangle is 1300 and one of the interior opposite angle is 600. Find the other interior opposite angle.

 · 2015-11-02 · Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Step 3 Complete the proof

 · 2015-11-02 · Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Step 3 Complete the proof

 · Web viewChapter 3/4: Probability and Counting 3.1/3.2 – Triangle Sum, Exterior Angle, Exterior Angle Inequality, and Triangle inequality Theorems The Triangle Sum Theorem states:

 · Web viewChapter 3/4: Probability and Counting 3.1/3.2 – Triangle Sum, Exterior Angle, Exterior Angle Inequality, and Triangle inequality Theorems The Triangle Sum Theorem states:

Obj. 15 Triangle Angle Relationships

Obj. 15 Triangle Angle Relationships

Mrs. Newbold Bingham Math - Home...9x-2 a) Find x. 5 Exterior Angle Theorem: The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior

Mrs. Newbold Bingham Math - Home...9x-2 a) Find x. 5 Exterior Angle Theorem: The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior