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4-2_Triangle_sum.ppt

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This document discusses classifying triangles by angles and sides, the triangle interior angle sum theorem, and the exterior angle theorem. It defines acute, obtuse, right, equilateral, isosceles, and scalene triangles. It states that the sum of the interior angles of any triangle is 180 degrees. It introduces the exterior angle theorem, which states that an exterior angle of a triangle is equal to the sum of the two remote interior angles. The document provides examples of using these triangle theorems and properties to find missing angle measures.

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CLASSIFYING TRIANGLES and THE TRIANGLE INTERIOR ANGLE SUM THEOREM Jim Smith 4-1 and 4-2 3108.4.9
Classifying by Angles Acute Triangle Has three acute angles Obtuse Triangle Has one obtuse angle Right Triangle Has one right angle
Classifying by sides Equilateral Triangle All three sides are congruent Isosceles Triangle Two of the sides are congruent Scalene Triangle No sides are congruent
Classify the triangle by the sides and angles. 8 in 8 in Isosceles right triangle Equilateral acute triangle
Classify each triangle by its sides and angles. Isosceles obtuse triangle Scalene obtuse triangle Scalene right triangle
If you add up the measures of the interior angles of a triangle, What is the total? 180尊 25尊 65尊
How many lines can be drawn through point B that would become parallel to M m B
Unique Parallel line Postulate Through a point not on a given line, there is one and only one line parallel to the given line. m B
Given: Prove: 1. ABC is a triangle 2. Draw helping line through B so that 3. 4. 5. 6. 7. 1. Given 2. Unique Parallel Postulate 3. Def of Straight Angles 4. Angle Addition Postulate 5. Substitution 6. 2 ll Lines, Alt Int Angles Congruent 7. Substitution Property 1 2 3 180 m m m || DE AC DE B C A 2 1 3 180 m DBE 4 2 5 m DBE m m m D E 4 5 4 2 5 180 m m m 1 4; 3 5 m m m m 1 2 3 180 m m m ABC
How can we use this? The ladder is leaning on the ground at a 75尊 angle. At what angle is the top of the ladder touching the building? 75 75 90 180 165 180 15 x x x 15
Find the missing angle. 43 47
Find the value of X. 30属 X-8 2x+28 X-8 + 2x+28 + 30 = 180属 3x + 50 = 180 3x = 130 X = 43.33属
Find the missing angles. 55属 25属 y属 w属 x属 120属 W = 35属 X = 35属 Y = 120属
Exterior Angle Theorem An exterior angle of a triangle is equal in measure to the sum of the measures of its two remote interior angles. Exterior Remote Interior Adjacent Interior ( An exterior angle and its adjacent interior angle are supplementary )
Given: ABC with exterior Prove: 1. ABC is a triangle with exterior angle 4. 2. 3. 4. 5. 6. 7. 1. Given 2. Straight Angle Postulate 3. Angle Addition Postulate 4. Substitution 5. Triangle Sum Theorem 6. Substitution Property 7. Subtraction Prop. Of Equality 4 1 2 m m m 180 m BCD C D 3 4 m BCD m m 3 4 180 m m 1 2 3 180 m m m 3 4 1 2 3 m m m m m 4 1 2 m m m 4 A B 2 1 3 4
Find the missing angles measurements (<1 and <2). 120尊 55尊 35 2 1 remote interior angles < 1 = 90 + 55 < 2 = 120 + 35
For Warm-up 70属 y属 z属 w属 D E 50属 x属 (x-30)属 x属 70属 60属 50属 110属 D E 50属 70属 (80-30)属 80属 3X 60 = 180 > >
1 3 2 59属 47属 64属 1 2 3 28属 46属 55属

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4-2_Triangle_sum.ppt

  • 1. CLASSIFYING TRIANGLES and THE TRIANGLE INTERIOR ANGLE SUM THEOREM Jim Smith 4-1 and 4-2 3108.4.9
  • 2. Classifying by Angles Acute Triangle Has three acute angles Obtuse Triangle Has one obtuse angle Right Triangle Has one right angle
  • 3. Classifying by sides Equilateral Triangle All three sides are congruent Isosceles Triangle Two of the sides are congruent Scalene Triangle No sides are congruent
  • 4. Classify the triangle by the sides and angles. 8 in 8 in Isosceles right triangle Equilateral acute triangle
  • 5. Classify each triangle by its sides and angles. Isosceles obtuse triangle Scalene obtuse triangle Scalene right triangle
  • 6. If you add up the measures of the interior angles of a triangle, What is the total? 180尊 25尊 65尊
  • 7. How many lines can be drawn through point B that would become parallel to M m B
  • 8. Unique Parallel line Postulate Through a point not on a given line, there is one and only one line parallel to the given line. m B
  • 9. Given: Prove: 1. ABC is a triangle 2. Draw helping line through B so that 3. 4. 5. 6. 7. 1. Given 2. Unique Parallel Postulate 3. Def of Straight Angles 4. Angle Addition Postulate 5. Substitution 6. 2 ll Lines, Alt Int Angles Congruent 7. Substitution Property 1 2 3 180 m m m || DE AC DE B C A 2 1 3 180 m DBE 4 2 5 m DBE m m m D E 4 5 4 2 5 180 m m m 1 4; 3 5 m m m m 1 2 3 180 m m m ABC
  • 10. How can we use this? The ladder is leaning on the ground at a 75尊 angle. At what angle is the top of the ladder touching the building? 75 75 90 180 165 180 15 x x x 15
  • 11. Find the missing angle. 43 47
  • 12. Find the value of X. 30属 X-8 2x+28 X-8 + 2x+28 + 30 = 180属 3x + 50 = 180 3x = 130 X = 43.33属
  • 13. Find the missing angles. 55属 25属 y属 w属 x属 120属 W = 35属 X = 35属 Y = 120属
  • 14. Exterior Angle Theorem An exterior angle of a triangle is equal in measure to the sum of the measures of its two remote interior angles. Exterior Remote Interior Adjacent Interior ( An exterior angle and its adjacent interior angle are supplementary )
  • 15. Given: ABC with exterior Prove: 1. ABC is a triangle with exterior angle 4. 2. 3. 4. 5. 6. 7. 1. Given 2. Straight Angle Postulate 3. Angle Addition Postulate 4. Substitution 5. Triangle Sum Theorem 6. Substitution Property 7. Subtraction Prop. Of Equality 4 1 2 m m m 180 m BCD C D 3 4 m BCD m m 3 4 180 m m 1 2 3 180 m m m 3 4 1 2 3 m m m m m 4 1 2 m m m 4 A B 2 1 3 4
  • 16. Find the missing angles measurements (<1 and <2). 120尊 55尊 35 2 1 remote interior angles < 1 = 90 + 55 < 2 = 120 + 35
  • 17. For Warm-up 70属 y属 z属 w属 D E 50属 x属 (x-30)属 x属 70属 60属 50属 110属 D E 50属 70属 (80-30)属 80属 3X 60 = 180 > >