MATHEMATICS UT 4.1

• Parts of Right Triangle

  A) acute angle

  B) acute angle

  C) 90 degrees

  D) hypotenuse

  E) leg

  F) leg

  G) longest side

  H) sides

  
• Triangle Congruence Postulate/Theorem

  A) SAS

  
• Triangle Congruence Postulate/Theorem

  A) SSS

  
• Triangle Congruence Postulate/Theorem

  A) ASA

  B) vertical angles

  
• Triangle Congruence Postulate/Theorem

  A) LL

  
• Finding X

  A) 10

  
• Find the Side

  A) 17

  
• Summary of Angles in Triangle

  A) 180

  B) 180

  C) exterior angle

  D) 360

  E) d=a+b

  
• Sum of the interior angles of a triangle

  Always 180°

  
• Sum of the exterior angles of a triangle

  Always 360°

  
• Exterior angle theorem


  The exterior angle of a triangle is equal to the sum of two opposite interior angles

  
• Solve for the missing exterior or interior angle of each triangle


  1. 122° - 90° = 32°, x = 32°

  2. 34° + 21° = 55°, x° = 55°

  3. 94° - 60° = 34°, x = 17°

  4. 100° - 51° = 49°, 2x + 3° = 49°, x = 23°

  
• Triangle inequality theorem


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

  
• Determine whether the given set of sides form a triangle

  • 4 CM - 7 CM - 5 CM, Yes it does form a triangle
  • 12 meters beam on each side, Possible range: 0<3rd Side<24
  • 10. 8 meters - 6 meters, Possible range: 2<3rd Side<14

  
• Angle-side relationship theorem


  In a triangle the side opposite the larger angle is the longer side

  
• List the sides in order from longest to shortest

  • 110° + 28° = 138°, 180° - 138° = 42°, Ans: HG, FG, FH
• Exterior angle inequality theorem


  The exterior angle of a triangle is greater than any one of the two remote interior angles

  
• Hinge theorem


  If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle

  
• Converse of hinge theorem (S.S.S.)


  If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side

  
• Solve for the range of possible values for x

  1. 12. 0 < (5x - 20)° < 60°, Possible answers: 4 < x < 16

  2. 13. (3x - 5)° > 16°, Possible answer: x > 7