SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Understanding Triangle Inequality Theorems: The Key to Geometric Relationships

katalin-molnar avatar
katalin-molnar
17 diapositives · 259 Views · Nov 09, 2014

Explore the concept of inequality in triangles through the Triangle Inequality Theorem and related principles such as SAS and SSS inequalities. Learn how to prove geometric relationships using indirect proofs. Homework includes practice problems for in-depth understanding.

Understanding Triangle Inequality Theorems: The Key to Geometric Relationships - slide 1
01 / 17Understanding Triangle Inequality Theorems: The Key to Geometric Relationships
1 / 17

Télécharger la présentation

Understanding Triangle Inequality Theorems: The Key to Geometric Relationships
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Chapter 6 Review

  2. DEFINITION OF INEQUALITY • Difference in size, degree or congruence 70 B 20 A

  3. ADDITION POI THEN IF and EXAMPLE: IF and THEN

  4. Multiplication POI THEN IF and EXAMPLE: IF and THEN

  5. Multiplication POI THEN IF and EXAMPLE: IF and THEN

  6. DIVISION POI THEN IF and EXAMPLE: IF and THEN

  7. DIVISION POI THEN IF and EXAMPLE: IF and THEN

  8. Transitive POI THEN IF and EXAMPLE: IF and THEN

  9. POI THEN IF and EXAMPLE: IF and THEN

  10. Exterior angle inequality theorem The measure of an exteriorangle of a triangle is greater than the measure of eitherremoteinterior angle. and 2 1 4

  11. Indirect Proofs 1. Assume temporarily that the conclusion is nottrue. 2. Reason logically until you reach a contradiction of a known fact. 3. State that the temporaryconclusion is false. 4. Therefore the original conclusion must be true.

  12. THEOREM: If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side. What you need to understand: The angle opposite the longest side in a triangle is the largest angle. <B is opposite the largest side. Therefore, <B is the largest angle. B 10 4 A C 12

  13. Conversely, the largestside is across from the largestangle. AC is the longest side. 85 B 65 30 A C

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

  15. SAS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

  16. SSS Inequality Theorem If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second.

  17. HOMEWORK • PG 630 • 1-12 all • PG 631 • 1-11 (omit 4, 5 and 8) • Worksheets (green and blue)