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Geometry

Today: Class Attendance / Announcements Return / Review Chapter 3 Tests 4.1 Notes / Break / 4.2 Notes Exit Slip Begin Homework. Be not afraid of going slowly; be afraid only of standing still. Chinese Proverb. Geometry. 4.1/4.2 Triangles and Angles. Objectives: Classify triangles

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Geometry

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  1. Today: Class Attendance / Announcements Return / Review Chapter 3 Tests 4.1 Notes / Break / 4.2 Notes Exit Slip Begin Homework Be not afraid of going slowly; be afraid only of standing still. Chinese Proverb Geometry

  2. 4.1/4.2 Triangles and Angles Objectives: • Classify triangles • Find angle measures in a triangle • Identify congruent figures and corresponding congruent parts • Prove triangles are congruent • Know 3 basic properties of triangles in a triangle Vocabulary: equilateral, isosceles, scalene, acute, equiangular, right, obtuse, interior angles, exterior angles

  3. C A B 4.1 Classifying Triangles Triangle: Triangle Sum Theorem: Triangle: 3 sided closed figure. Triangle Sum Theorem: The sum of the measures of a triangle is 180º. Examples: Find the measure of 1. 1. 2. Why? 

  4. B Y A X C Z 4.2 Congruence and Triangles Triangle Sum Theorem: The sum of the measures of a triangle is 180º. Third Angle Theorem: If two angles in one triangle are congruent to two angles in another triangle, then the third angles are also congruent.

  5. Use it in PROOF!!! Given: MNO  PQO Prove: NMO  QPO

  6. 5 Essential Parts of a Proof. • List the given information. • Identify conclusion to be proven. • If possible, draw and mark a picture. • Develop a system of reasoning. • End with the idea to be proven.

  7. Use it in PROOF!!! • Given: MNO  PQO • Prove: NMO  QPO • Statements Reasons • MNO  PQO 1) Given • MON  POQ 2) Vertical Angles are Congruent • NMO  QPO 3) Third Angle Theorem

  8. Use it with Algebra. Find the value of x: (4x – 15)º F B 87º 22º A D E C

  9. Take a quick break. Get up, stretch out, talk to a neighbor, or try the following rebus puzzles… Break Time Beaten black and blue Middle C

  10. 2 3 4 1 Connections Old Information: Put it together: Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures the two nonadjacent interior angles.

  11. Applying the Exterior Angle Theorem x 72o (2x – 11) Find the measure of 1. 1. 2. Find the value of x. 

  12. Labeling Triangles Vertex: Adjacent Side: Opposite Side: Name the sides that are opposite and adjacent to each vertex. Vertex: points joining the sides of the triangle. Adjacent Side: sides sharing a common vertex. Opposite Side: side opposite from the vertex.

  13. F B E C A D Congruent Triangles Congruent Figures: Corresponding Sides: Corresponding Angles: Congruent Triangles: Congruent Triangles also known as a congruency statement.

  14. R 36° 54° S Q Classify by Angles Right: Classify ΔQRS Obtuse: Acute: Equiangular: Right: contains one right angle. Obtuse: contains one obtuse angle. Acute: contains three acute angles. Equiangular: contains three congruent angles. contains three 60° angles.

  15. A B C Classify By Sides Equilateral: Classify ΔABC Isosceles: Scalene: Equilateral: all sides congruent. Isosceles: at least two sides congruent. Scalene: no sides congruent.

  16. Keep going… Corollary to the Triangle Sum Theorem: The acute angles of right triangle are complementary. Examples: Find the measure of 1. 1. 2. A C B 

  17. Before you leave, complete the following exit slip. PUT SOME THOUGHT INTO THIS! List 3 things you learned from today’s lesson. List 2 concepts/ideas you thought were confusing. List 1 thing you can do to understand the confusing/difficult concepts better. 3-2-1 Exit Slip

  18. Assignment: 4.1, 4.2 pgs. 198-200 #19-26, 31-39, 41-43, 47 Quiz 4.1-4.4 Friday Geometry Be not afraid of going slowly; be afraid only of standing still. Chinese Proverb

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