Target 5.4: Use angle properties in triangles to determine unknown angle measurements 5.4: Parallel Lines and Triangles
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1 Unit 5 Parallel and Perpendicular Lines Target 5.1: Classify and identify angles formed by parallel lines and transversals 5.1 a Parallel and Perpendicular lines 5.1b Parallel Lines and its Angle Relationships Target 5.2: Apply and prove statements using perpendicularity theorems 5.2a Prove Theorems about Perpendicular Lines 5.2b Constructions: Perpendicular and Parallel Lines Target 5.3 : Use parallel and perpendicular lines to write linear equations and to determine the distance between a point and a line 5.3a Determine Whether Lines are Parallel or Perpendicular Using Linear Equations 5.3b Determine Whether Lines are Parallel or Perpendicular Using Linear Equations Target 5.4: Use angle properties in triangles to determine unknown angle measurements 5.4: Parallel Lines and Triangles Date Target Assignment to be Completed Before Class Video? In Class Assignment Done? M a 5.1a Video 5.1a Worksheet T b 5.1b Video 5.1b Worksheet W a 5.2a Video 5.2a Worksheet R b 5.2b Video 5.2b Worksheet F a 5.3a Video 5.3a Worksheet M b 5.3b Video 5.3b Worksheet T Review Review W Quiz Quiz M Video 5.4 Worksheet T 12-1 Quiz Quiz 5.4 W 12-2 Review Unit 5 Review R 12-3 Test Unit 5 Test NAME:
2 5.1a Draw and Classify Angles formed by Transversals Target 1: Classify and find measures of angles formed by parallel lines and transversals Vocabulary: Parallel Lines: Example 1: Identify relationship in space Think of each segment in the figure as part of a line. Which lines(s) or plane(s) in the figure appear to fit the description? a) Line(s) parallel to AFand containing point E. b) Plane(s) parallel to plane FGJ and containing point E. Drawing with your teacher! What is a way you can tell that lines are parallel in a diagram?
3 Example 2: Identify angle relationships Identify the special angle pairs in the diagram a) Corresponding Angles b) Alternative Interior Angles c) Alternate Exterior Angles d) Consecutive Interior Angles YOU TRY NOW! 1) Identify special angle pair relationships in the diagram Were you able to identify all of the angle pairs WITHOUT looking at the answers first? a) Corresponding Angles b) Alternative Interior Angles c) Alternate Exterior Angles d) Consecutive Interior Angles
4 5.1b Use Parallel Line and Transversals Target 1: Classify and find measures of angles formed by parallel lines and transversals Congruent Angle Pairs Supplementary Angle Pairs If are intersected by a transversal, then Corresponding Angles are Congruent Consecutive Interior Angles are Supplementary What do supplementary angles add up to? Alternate Interior Angles are Congruent Alternate Exterior Angles are Congruent What does congruent mean? Example 1: Identify Congruent Angles The measure of three of the number angles is 125. Identify those angles. For each pair of angles, identify which angles are congruent and explain why. Which angles are supplementary?
5 Example 2: Use properties of parallel lines Find the value of x, then find the measure of angle 2. YOU TRY NOW! 1) If the m 7 = 75, what other angles are congruent to 7? Explain how you know. Name all vertical angles in the diagram. Congruent Angles: Explanation: 2) A taxiway is being constructed that intersects two parallel runways at an airport. You know that m 2 = 98. What is m 1? How do you know? 3) Find the value of x and explain your reasoning for your initial equation.
6 5.2a Prove Theorems about Perpendicular Lines Target 2: Apply and prove statements using perpendicularity theorems Vocabulary/Concept Draw a horizontal line below and draw a smiley face somewhere above the line. How would you calculate the shortest diance from the smile face to the line? Angles Formed with Perpendicular lines What symbol would you see that IMMEDIATELY indicates that two lines are intersecting? Linear Pairs of Congruent Angles If two lines intersect to form a of congruent angles, then. Apply and prove statements using perpendicularity theorems Perpendicular Lines and Right Angles Theorem If two lines are perpendicular, then. Example 1: Explain how you know that angles have specific properties In the diagram, 1 2. Prove that 3 and 4 are complementary using complete sentences.
7 YOU TRY NOW! 1) If c d, what do you know about the sum of the measure of 3 and 4? Answer in complete sentences 2) Determine which lines, if any, must be parallel in the diagram. Explain
8 5.2b Constructions: Perpendicular and Parallel Lines Target 2: Apply and prove statements using perpendicularity theorems Constructions of Perpendicular lines Example 1: Construct a perpendicular line from a point on line Video: The perpendicular from a point on a line Example 2: Construct a perpendicular line to the original line and that passes through a given point not on the line. Video: Construction 4 Perpendicular to Line Through Point Not on Line
9 Constructions of Parallel Lines Example 3: Construct a line parallel to a given line Video: Constructing Parallel Lines (using a straightedge and a compass) Example 4: Construct a line parallel to a given line through a specific point Video: Constructing Parallel Line Through a Given Point
10 5.3a Determine Whether Lines are Parallel or Perpendicular Using Linear Equations Target 3: Use parallel and perpendicular lines to write linear equations and to determine the distance between a point and a line Parallel Lines If two NONVERTICAL lines have the same, then the lines are. Given Line: y = 3x + 1 Line 1: Line 2: Example 1: Write an equation of a parallel line Write an equation of the line that passes through (2, 4) AND is parallel to the line y = 4x + 1.
11 Perpendicular Lines If two NONVERTICAL lines have the slopes that are, then the lines are. **opposite reciprocal example Given Line: y =!! x 2 Line 1: Line 2: Example 2: Determine parallel or perpendicular lines Determine which lines of the following lines, IF ANY, are parallel or perpendicular: Line a: 12x 3y = 3 Line b: y = 4x + 2 Line c: 4y + x = 8 YOU TRY NOW! 1) Write an equation of the line that passes through (-4, 6) and is parallel to the line y = 3x + 2 2) Determine which of the following lines, if any, are parallel or perpendicular. Line a: 4x + y = 2 Line b: 5y + 20x = 10 Line c: 8y = 2x + 8
12 YOU TRY NOW! (cont) 3) Write an equation of a perpendicular line Write an equation of the line that passes through (-3, 4) and is perpendicular to the line y =!! x + 2.
13 5.3b Determine Whether Lines are Parallel or Perpendicular Using Linear Equations Target 3: Use parallel and perpendicular lines to write linear equations and to determine the distance between a point and a line VIDEO: MPM2D-2.1- Finding Distance Between a Point and a Line Example 1: Calculate the shortest distance between point A(6, 5) and the line y = 2x + 3. YOU TRY NOW! Calculate the shortest distance between point A(1, 5) and the line y = 5x 2.
14 5.4 Parallel Lines and Triangles Target 4: Use angle properties in triangles to determine unknown angle measurements Vocabulary Triangle: Interior Angles: Exterior Angles: Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the SUM of the measures of the two angles. Example 1: Find the measure of DCB. YOU TRY NOW! Find the measure of 1 in the diagram shown.
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