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+ Angles and Lines + What do we know about angles? + Where can we see angles in everyday life? + Important Vocabulary Vertex Ray Angles Right Angles Acute Angles Obtuse Angles Straight Angles Complementary Angles Supplementary Angles + Vertex Vertex- A point where two or more straight lines or rays meet + Which is the vertex? + Ray A line with a start point but no end point + Angles The amount of turn between two straight lines that have a common end point (the vertex). + Where are the angles? + Naming Angles To name an angle we use the outermost points on the rays and the vertex. Angle GHF Angle FHG GHF FHG + You Try! Name the angles D F E + Right Angle Right angle-An angle which is equal to 90° + Acute Angle Acute angle- an angle that is less than 90° + Obtuse Angles Obtuse Angle- an angle that is greater than 90° but less than 180° + Straight Angle Straight Angle- an angle that is 180° exactly + Time to Practice! + Name and Classify + Complementary Angles Complementary Angles- angles that are next to each other and add up to 90° + Which are Supplementary Angles? Supplementary Angles-when two angles add up to 180 degrees + What is the missing measure? To find the missing measure we need to follow these steps: 1. Identify as complementary or supplementary 2. Subtract + Find the Missing Measure + Find the Missing Measure + Find the Missing Measure + Find the Missing Measure + Let’s Practice + Let’s Practice + Lines To name a line you use the outermost point Indicates by the arrows on both sides + Lines A straight series of points that has no start point or not end point and put a line with arrows above it PQ QP + Name the following Lines + Types of Lines Parallel Lines Perpendicular Lines Intersecting + Parallel Lines are always the same distance apart (called "equidistant"), and will never meet + Which are Parallel Lines + Naming Parallel Lines To name parallel lines we name each line individually (outermost points) To indicate lines are parallel we use the Example: AB CD symbol + Practice Name the following parallel lines + Perpendicular Lines Lines that are at right angles (90°) to each other when they intersect + Which are perpendicular lines? + Naming Perpendicular Lines To name perpendicular lines we name each line individually (outermost points) To indicate lines are perpendicular we use the Example: AB CD symbol + Name the Following + Which is which? + Intersecting Lines Lines that overlap or cross at a specific point, called the intersect + New Vocabulary Congruent Transversal Vertical Angles Adjacent Angles Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Interior Angles + Congruent The same size + Transversal A line that crosses a set of parallel lines + Vertical Angles Vertical Angles are the angles opposite each other and share the same vertex vertical angles are equal + Corresponding Angles The angles in matching corners are called Corresponding Angles. Think about if you cut and placed + Alternate Interior Angles The pairs of angles on opposite sides of the transversal but inside the two lines are called Alternate Interior Angles. Alternate Interior angles are congruent + Alternate Interior Angles 3 6 5 4 + Alternate Exterior Angles The pairs of angles on opposite sides of the transversal but outside the two lines are called Alternate Exterior Angles. These angles are congruent + Alternate Exterior Angles 2 8 1 7 + Consecutive Interior Angles The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles. Their sum is 180° + Consecutive Interior Angles + Adjacent Angles Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap. Angle ABC is adjacent to angle CBD Because: they have a common side (line CB) they have a common vertex (point B) + Adjacent Angles Adjacent Angles 1 and 2 3 and 4 5 and 6 7 and 8 + Which is which? Vertical Corresponding Alternate Exterior Adjacent Alternate Interior Consecutive + Practice Vertical Corresponding Alternate Exterior Adjacent Alternate Interior Consecutive + Practice Vertical Corresponding Alternate Exterior Adjacent Alternate Interior Consecutive + Practice Vertical Corresponding Alternate Exterior Adjacent Alternate Interior Consecutive + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure? 5 + What is the missing measure? + What is the missing measure? E= 150 + What is the missing measure? 0 + What is the missing measure? 0 + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure? + What is the missing measure?