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Chapter 7 : GEOMETRY Section 3

Chapter 7 : GEOMETRY Section 3. TRIANGLES. California Standards. Measurement and Geometry 2.0: Students identify and describe the properties of 2 - dimensional figures. Measurement and Geometry 2.3:

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Chapter 7 : GEOMETRY Section 3

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  1. Chapter 7: GEOMETRYSection 3 TRIANGLES

  2. California Standards • Measurement and Geometry 2.0: • Students identify and describe the properties of 2-dimensional figures. • Measurement and Geometry 2.3: • Identify angles as VERTICAL, ADJACENT, COMPLEMENTARY, or SUPPLEMENTARY and provide descriptions of these terms.

  3. Key Vocabulary • TRIANGLE: A polygon formed by three straight segments. • SCALENE: Possessing NO sides that are EQUAL in measurement. • ISOSCELES: Possessing 2 sides and 2 angles that are EQUAL to each other. • EQUILATERAL: Possessing ALL sides EQUAL to each other. • ACUTE: A term that refers to the measure of an angle. • If an angle is ACUTE, it simply means that the angles possesses a measure GREATER than 0° but LESS than 90°. • RIGHT: A term that refers to an angle equaling EXACTLY 90° • OBTUSE: A term that refers to the measure of an angle. • If an angle is OBTUSE, it simply means that the angles possesses a measure GREATER than 90° but LESS than 180°. • CONGRUENT: CONGRUENT is a term that is used to describe EQUALITY. • Here, if sides or angles are CONGRUENT, they possess the same measurement.

  4. What is a TRIANGLE? • A TRIANGLE is a polygon. A polygon is a closed geometric figure made of line segments. A TRIANGLE is also known as a TRIGON. This means its made up of 3 line segments. • TRIANGLES are traditionally named with 3 capital letters. These 3 lettered points are the vertices or endpoints of the line segments. • TRIANGLES possess 3 ANGLES and 3 SIDES. • The TOTAL Interior Measure of a TRIANGLE is 180°. • Basic Formula: Angle 1 + Angle 2 + Angle 3 = 180°

  5. CLASSIFYING TRIANGLES BY SIDES • Triangles can be classified by the MEASURE of their SIDES. • Using identified sides or measuring tools, you can use the measures of the sides to correctly classify a triangle. • Once the side measures are found, TRIANGLES fall into one of the following categories: • SCALENE: NOT A SINGLE SIDE MEASURES THE SAME. • ISOSCELES: A PAIR of sides is EQUAL to one another. • EQUILATERAL: ALL 3 sides are EQUAL to each other.

  6. CLASSIFYING TRIANGLES BY ANGLES • Triangles can be classified by the MEASURE of their ANGLES. • Using identified angles or measuring tools, you can use the measures of the angles to correctly classify a triangle. • Once the angle measures are found, TRIANGLES fall into one of the following categories: • ACUTE: The measure of the ANGLES all are UNDER 90°. • OBTUSE: The measure of one of the ANGLES is over 90° but under 180°. • RIGHT: The measure of one of the ANGLES is EXACTLY 90°.

  7. MEASURES of a TRIANGLE • The INTERIOR Measure of a Triangle ALWAYS equals 180°. • Any combination of angle measures can be combined. • Recall that the 3 angles will ALWAYS result in 180°. • The BASIC FORMULA is the following: • Angle 1 + Angle 2 + Angle 3 = 180° • Examples: 30° + 70° + 80° = 180° (ACUTE Triangle) 45° + 45° + 90° = 180° (RIGHT Triangle) 20°+45°+115° = 180° (OBTUSE Triangle)

  8. SOLVING FOR MISSING ANGLES • When you are solving for the missing angle within a Triangle, you will need to work carefully, using ALL known information and the BASIC FORMULA. Simple Algebra will also be used to solve correctly. • Example: There is a triangle where Angle 1 is 40° and Angle 2 is 65°. What is the measure of Angle 3? • Angle 1 + Angle 2 + Angle 3 = 180° -Basic Formula • 40° + 65° + Angle 3 = 180° -Drop in Known Angles • 105° + Angle 3 = 180° -Known Angles are combined -105° -105° -Solve Algebraically • Angle 3 = 75° -Result is the answer. • 40° + 65° + 75° = 180° -Double Check • 180° = 180° -Answer is CORRECT

  9. Finding MORE Angles • A Triangle exists. Angle 1 measures 85°. Angle 2 measures 25°.Please find the measure for Angle 3. • Angle 1+Angle 2+Angle 3=180° -Basic Formula is used • 85° + 25°+ Angle 3 = 180° -Drop in the known Angle Measure • 110° + Angle 3 = 180° -Solve Algebraically -110°-110° • Angle 3 = 70°-Result is your answer • A Triangle exists. Angle 1 measures 47°. Angle 2 measures 78°.Please find the measure for Angle 3. • Angle 1+Angle 2+Angle 3=180° -Basic Formula is used • 47° + 78°+ Angle 3 = 180° -Drop in the known Angle Measure • 125° + Angle 3 = 180° -Solve Algebraically -125°-125° • Angle 3 = 55°-Result is your answer

  10. QUICK REVIEW • Classifying Triangles by SIDE Measures: • There are 4 ways an Angle can be classified as: • SCALENE: Not a single side is EQUAL. All are DIFFERENT Measures. • ISOSCELES: 2 Sides are EQUAL in Measure. • EQUILATERAL: ALL 3 sides are EQUAL in Measure. • Classifying Triangles by ANGLE Measures: • There are 4 ways an Angle can be classified as: • ACUTE: Angles within the Triangle measure UNDER 90°. • OBTUSE: One angle within the Triangle is Over 90° but Under 180°. • RIGHT: EXACTLY 90°. • Interior Measure of a TRIANGLE: Angle 1+Angle 2+Angle 3 = 180°

  11. Check for Understanding • Please determine the BEST answer for the following expression. • Carry out ALL work and calculations in your NOTES for later reference • Please write your answer on your wipe boards and wait for the teacher’s signal. • On the count of 3, hold up your wipe boards.

  12. C4U Question #1 • Question #1: • A Triangle exists where a pair of sides is EQUAL in measure. What type of Triangle is this? • Please work out the problem within your notes • Write the correct answer on your wipe board. • Wait for Teacher’s Signal.

  13. C4U Question #2 • Question #2: • A Triangle exists where one of the angles is 103° in measure, and the other two angles are 27° and 50°. What type of Triangle is this? • Please work out the problem within your notes • Write the correct answer on your wipe board. • Wait for Teacher’s Signal.

  14. C4U Question #3 • Question #3: • A Triangle exists where 2 angles are known. Angle 1 measures 53°. Angle 2 measures 72°. Please find the measure for Angle 3. • Please work out the problem within your notes • Write the correct answer on your wipe board. • Wait for Teacher’s Signal.

  15. C4U Question #4 • Question #4: • A Triangle exists where 2 angles are known. Angle 1 measures 53°. Angle 2 measures 72°. Please find the measure for the Angle 3. • Please work out the problem within your notes • Write the correct answer on your wipe board. • Wait for Teacher’s Signal.

  16. GUIDED PRACTICE • Students will work on a worksheet/book work, focusing only on the problems assigned by the teacher. • Work carefully, show your problem solving process, and double check all calculations. • Use scratch paper to carry out your work. • Once you have completed the assigned problems, please raise your pencil. • The teacher will then check your work and release you to complete the independent practice.

  17. INDEPENDENT PRACTICE • Once you have been signed off and released to complete Independent Practice, please complete the following assignment:

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