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Transcript
Section: 3-1 Name: Topic: Properties of Class: Geometry 1A Parallel Lines Period: Standard: 1 Date: Transversal A transversal is a line that intersects two coplanar lines at two distinct points. 2 3 1 4 5 8 7 6 How many angles are formed? There are _____ angles. ______________________________________________________ Exterior Angles The exterior angles are ________________________________. Interior Angles The interior angles are ________________________________. Alternate Interior Angles ____ and _____ are alternate interior angles. Name another Alternate means ______________ pair of alternate interior angles. ____ and _____ Alternate Exterior Angles ____ and _____ are alternate exterior angles. Name another pair of alternate exterior angles. ____ and _____ Corresponding Angles ____ and _____ are corresponding angles. Name three more pairs of corresponding angles. ____ and _____ ____ and _____ Same-Side Interior Angles ____ and _____ ____ and _____ are same-side interior angles. Name another pair of same-side interior angles. ____ and _____ 1 What happens to the angles when the lines are parallel? 1. Draw any non-perpendicular transversal. 2. Label two corresponding angles as 1 and 2. 3. Use patty paper to measure the opening of 1. How does the measure of 1 compare to the measure of 2? Corresponding Angles The corresponding angles formed by parallel lines and a transversal are ___________________________. m n m n Alternate Interior Angles 1. Draw any non-perpendicular transversal. 2. Label two alternate interior angles as 3 and 4. 3. Use patty paper to measure the opening of 3. How does the measure of 3 compare to the measure of 4? The alternate interior angles formed by parallel lines and a transversal are ___________________________. m m n n 2 Alternate Exterior Angles 1. Draw any non-perpendicular transversal. 2. Label two alternate exterior angles as 5 and 6. 3. Use patty paper to measure the opening of 5. How does the measure of 5 compare to the measure of 6? The alternate exterior angles formed by parallel lines and a transversal are ___________________________. m n m n What about same-side interior angles? Are they congruent too? m 8 7 9 m n n We know that 7 _____ and 7 + _____ = 180. By substitution _____ + _____ = 180. Therefore same-side angles formed by parallel lines are _______________________________. Summary/Reflection: The letters Z, F and C can be used to help you identify types of angles. Name the type of angle illustrated by each letter. 3 Section: 3-2 Name: Topic: Proving Lines Class: Geometry 1A Parallel Period: Standard: Date: How do we know a b ? How can we PROVE a b ? b 150 10x 2x a To PROVE two lines are parallel we must use information we KNOW to be true. Use this fact to determine x and then substitute back into the diagram. What is true about the diagram above? _____________________________________ To PROVE two lines are parallel you can use one of the following. If _________________________ angles are congruent, then the lines are parallel. If _________________________ angles are congruent, then the lines are parallel. If _________________________ angles are supplementary, then the lines are parallel. Summary/Reflection: In the diagram below, what does x have to be for r s ? 45 (2x-5) s r 4 Section: 3-3 Name: Topic: Triangles, Parallel Class: Geometry 1A Lines & the Triangle Angle- Period: Sum Theorem Date: Standard: Types of Triangles Classify by Angles Classify by Sides Sum of the Interior Angles of a Triangle ACUTE RIGHT OBTUSE EQUILATERAL ISOSCELES SCALENE 1. 2. 3. 4. 5. Trace the triangle you were given in the space below. Identify the triangle (by sides and angles). Label the angles as 1, 2 and 3. Tear off the angles and label the empty spaces as 1, 2 and 3. Line up vertices of the three angles and make them share sides. What is the sum of the interior angles of a triangle? __________ 5 Triangle Angle-Sum Theorem Examples All the angles in a triangle add up to ____________. 1. 3x 2x x 2. y 20 Exterior Angles of a Triangle What do we know about the triangle below? What else can we conclude? 4 1 2 3 The ___________________ angle equals the sum of the ____________________ interior angles. 6 Examples 1. What is the value of x? x 52 115 2. ABC is isosceles with AB the base. AC = 3x, AB = 10 and BC = 45. What is the value of x? C A B Summary/Reflection: Draw each triangle below or tell why it is impossible to draw. A. Isosceles right triangle B. Scalene obtuse triangle C. Right obtuse triangle D. Equilateral right triangle 7 Section: 5-5 Topic: Inequalities in Triangles Standard: 6 Name: Class: Geometry 1A Period: Date: Triangle Inequality Theorem The __________________ of the lengths of any 2 sides of a triangle is __________________________ the length of the third line. a + b > ________ b + c > ________ a + c > ________ a Example 1 b c Will a 3 inch, 6 inch, and 8 inch sticks form a triangle? Check conditions: 3 + 6 ______ 8 6 + 8 ______3 3 + 8 ______6 Example 2 What size stick could you use to create a triangle with 2 inch and 7 inch sticks? Any stick _________________ _________________ and ________________ inches. In symbols _____________________. 8 One Triangle Inequality Theorem Use a ruler to draw an obtuse scalene triangle in the space below. Then use a ruler and protractor to determine the side lengths and angle measures. The longest side is across from the ___________________ angle. The shortest side is across from the ___________________ angle. Example 3 Which angle is the largest in each triangle? B 4 S C 9 10 11 7 T U 9 A 9 Two Triangle Inequality, also known as The _________________ Theorem T P U S Q R If R is greater than Q then TU is _________ than PS. Note: The angle must be _______________ the marked sides. Example 4 If AB = FE and AC = FG, what is true about BC and EG? B E 65 C A 70 F G Summary/Reflection: Which side is the longest? C B 55 A 70 60 D 30 60 50 E 10 Section: 3-4 Name: Topic: The Polygon Angle- Class: Geometry 1A Sum Theorem Period: Standard: Date: Polygon Sketch Number of sides Number of triangles formed Sum of angle measures Number of interior angles If it was a regular polygon, measure of each int. angle Number of exterior angles Sum of measure of exterior angles Triangle 4 360 3 6 Heptagon 8 11 Angle-Sum Theorem One Angle of a Regular Polygon Interior Angles of a Polygon Exterior Angles of a Polygon Names of Polygons Number of Sides Name of Polygon 3 4 5 6 7 8 9 10 11 12 Example 1) If the measure of one interior angle of a regular polygon is 144, what is the name of the polygon? 12 2) The measure of an exterior angle of a regular polygon is 36 degrees. Name the polygon. 3) find the measure of one interior and one exterior angle in a 36-gon. 4) Solve for x x 2x 120 100 2x Summary/Reflection: If you forget the formulas above, explain how could you determine the sum of the angles of a dodecagon? 13