Concept. Example 1 Identify Possible Triangles Given Side Lengths A. Is it possible to form a triangle with the given side lengths of 6, 6, and 14 ? If.

Slides:

Advertisements

Similar presentations

Section 5-5 Inequalities for One Triangle

Advertisements

Apply inequalities in one triangle. Objectives. Triangle inequality theorem Vocabulary.

Objectives Apply inequalities in one triangle..

The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

Triangle Inequality Theorem:

5.5 Inequalities in Triangles

5-5 Indirect Proof and Inequalities in One Triangle Warm Up

5.4 The Triangle Inequality

5-5Triangle Inequality You recognized and applied properties of inequalities to the relationships between the angles and sides of a triangle. Use the Triangle.

Thursday, January 10, 2013 A B C D H Y P E. Homework Check.

Concept. Example 1 Identify Possible Triangles Given Side Lengths A. Is it possible to form a triangle with side lengths of 6, 6, and 14 ? If not, explain.

Triangle Inequality Theorem.  The sum of the two shorter sides of any triangle must be greater than the third side. Example: > 7 8 > 7 Yes!

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–2) NGSSS Then/Now Theorem 8.8: 45°-45°-90° Triangle Theorem Example 1:Find the Hypotenuse.

Lesson 4 Menu 1.Write the assumption you would make to start an indirect proof of the statement: ΔABC is congruent to ΔDEF. 2.Write the assumption you.

Vocabulary Triangle Sum Theorem acute triangle right triangle

Inequalities in One Triangle

5-Minute check……..APK Cond = H-C, Conv= C-H, Inverse = Not H – Not C, Contra = Not C – Not H.

Course: Applied Geometry Aim: What is Triangle Inequality Theorem Aim: What is Triangle Inequality? Do Now: Sketch 9.

Chapter 5 Section 5.5 Inequalities in a triangle.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

Triangle Inequalities. Definitions Theorem 5-12 Triangle inequality Theorem- Sum of the lengths of any two sides of a triangle is greater than the length.

The Triangle Inequality Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Lesson 5.4 The Triangle Inequality. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the.

4.7 Triangle Inequalities. In any triangle…  The LARGEST SIDE lies opposite the LARGEST ANGLE.  The SMALLEST SIDE lies opposite the SMALLEST ANGLE.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 5–4) CCSS Then/Now Theorem 5.11: Triangle Inequality Theorem Example 1:Identify Possible Triangles.

Warm Up 1. If ∆ABC  ∆DEF, then A  ? and BC  ?. 2. What is the distance between (3, 4) and (–1, 5)? 3. If 1  2, why is a||b? 4. List methods used.

Inequalities and Triangles

Lesson 5-4 The Triangle Inequality. 5-Minute Check on Lesson 5-3 Transparency 5-4 Write the assumption you would make to start an indirect proof of each.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 5–4) NGSSS Then/Now Theorem 5.11: Triangle Inequality Theorem Example 1: Identify Possible Triangles.

5-4 The Triangle Inequality. Triangle Inequality Theorem: The sum of two lengths in a triangle is always greater than the third length. Aulisio cut to.

1 Triangle Inequalities. 2 Triangle Inequality The smallest side is across from the smallest angle. The largest angle is across from the largest side.

Name the angles opposite of each side:  X is opposite of YZ  Y is opposite of XZ  Z is opposite of XY X Y Z.

1 Objectives State the inequalities that relate angles and lengths of sides in a triangle State the possible lengths of three sides of a triangle.

Geometry Section 5.5 Use Inequalities in a Triangle.

4.7 Triangle Inequalities

5.4 The Triangle Inequality What you’ll learn: 1.To apply the triangle inequality Theorem 2.To determine the shortest distance between a point and a line.

8.5 Proving Triangles are Similar. Side-Side-Side (SSS) Similarity Theorem If the lengths of the corresponding sides of two triangles are proportional,

5-5 Inequalities in One Triangle Warm Up Lesson Presentation

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–2) Then/Now Theorem 8.8: 45°-45°-90° Triangle Theorem Example 1:Find the Hypotenuse Length.

Date: 7.5 Notes: The Δ Inequality Lesson Objective: Use the Δ Inequality Theorem to identify possible Δs and prove Δ relationships. CCSS: G.C0.10, G.MG.3.

The Triangle Inequality LESSON 5–5. Lesson Menu Five-Minute Check (over Lesson 5–4) TEKS Then/Now Theorem 5.11: Triangle Inequality Theorem Example 1:Identify.

Inequalities in two triangles

5-5 Indirect Proof and Inequalities in One Triangle Warm Up

7-4 Triangle Inequality Theorem

5.6 and 5.7 Triangle Inequalities You found the relationship between the angle measures of a triangle. Recognize and apply properties of inequalities.

You found the relationship between the angle measures of a triangle. Recognize and apply properties of inequalities to the measures of the angles.

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

4-7 Warm Up Lesson Presentation Lesson Quiz Triangle Congruence: CPCTC

Section 5.5 Notes: The Triangle Inequality

Constructions!.

Kiley plans to fly over the route marked on the map of Hawaii.

Lesson 5-4 The Triangle Inequality

Inequalities and Triangles pp. 280 – 287 &

Triangle Inequalities

The Triangle Inequality

The Triangle Inequality

Honors Geometry.

TRIANGLE INEQUALITY THEOREM

Objectives Apply inequalities in one triangle..

Class Greeting.

Side – Angle Inequalities

GEOMETRY The Triangle Inequality

Side – Angle Inequalities

Vocabulary Indirect Proof

Five-Minute Check (over Lesson 5–4) Mathematical Practices Then/Now

Presentation transcript:

Concept

Example 1 Identify Possible Triangles Given Side Lengths A. Is it possible to form a triangle with the given side lengths of 6, 6, and 14 ? If not, explain why not. __ Check each inequality. Answer: X

Example 1 Identify Possible Triangles Given Side Lengths B. Is it possible to form a triangle with the given side lengths of 6.8, 7.2, 5.1? If not, explain why not. Answer: yes Check each inequality > > > > 5.1  12.3> 6.8  11.9> 7.2  Since the sum of all pairs of side lengths are greater than the third side length, sides with lengths 6.8, 7.2, and 5.1 will form a triangle.

A.A B.B Example 1 A.yes B.no

A.A B.B Example 1 A.yes B.no B. Is it possible to form a triangle given the side lengths 4.8, 12.2, and 15.1?

Example 2 In ΔPQR, PQ = 7.2 and QR = 5.2. Which measure cannot be PR? A 7 B 9 C 11 D 13

A.A B.B C.C D.D Example 2 A.4 B.9 C.12 D.16 In ΔXYZ, XY = 6, and YZ = 9. Which measure cannot be XZ?

Example 3 Proof Using Triangle Inequality Theorem TRAVEL The towns of Jefferson, Kingston, and Newbury are shown in the map below. Prove that driving first from Jefferson to Kingston and then Kingston to Newbury is a greater distance than driving from Jefferson to Newbury.

Example 3 Proof Using Triangle Inequality Theorem Answer: By the Triangle Inequality Theorem, JK + KN > JN. Therefore, driving from Jefferson to Kingston and then Kingston to Newbury is a greater distance than driving from Jefferson to Newbury. Abbreviating the vertices as J, K, and N: JK represents the side of the triangle from Jefferson to Kingstown; KN represents the side of the triangle from Kingston to Newbury; and JN the side of the triangle from Jefferson to Newbury.

A.A B.B Example 3 A.Jacinda is correct, HC + CG > HG. B.Jacinda is not correct, HC + CG < HG. Jacinda is trying to run errands around town. She thinks it is a longer trip to drive to the cleaners and then to the grocery store, than to the grocery store alone. Determine whether Jacinda is right or wrong.

Find the range of possible measures of x if each set of expressions represents measures of the sides of a triangle: 1. x, 4, 6 2 < x < 10

2.x – 2, 10, 12 4 < x < 24

3.x + 2, x + 4, x + 6 x > 0