Lesson 7 - Angle Relationships Notes PDF

Chapter 1 - Tools of Geometry Lesson 7: Angle Relationships ADJACENT ANGLES: two angles that lie in the same plane and have a common ___________ and common _____________, but NO other points in common. Example: N...

Chapter 1 - Tools of Geometry Lesson 7: Angle Relationships ADJACENT ANGLES: two angles that lie in the same plane and have a common ___________ and common _____________, but NO other points in common. Example: Non-example LINEAR PAIR: is a pair of ___________ angles with noncommon sides that are ___________ rays (lie on the ___________ line) Example: Non- example VERTICAL ANGLES: are two nonadjacent angles formed by two _________________ lines. They share a common ______________ and sides are ____________ ____________ **********Vertical angles are ________________ Example: Non-example Example 1: Vertical Angle Algebra Application Using the diagram to the right, find x, m∠AEC, and m∠BED A B (3x – 9)° (2x +13)° E C D x = ____________ m∠AEC =__________ m∠BED =__________ COMPLEMENTARY ANGLES: are TWO angles with measures that SUM to ______ degrees. Adjacent Example: Non-adjacent Example How to find the complement of an angle Example 2: Find the complement of a 20° angle. Example 3: Complementary Angles Algebra Application The measure of two complementary angles are 7x +17 and 3x – 20. Find the measures of each angle. SUPPLEMENTARY ANGLES: are TWO angles with measures that SUM to ______ degrees. Adjacent Example: Non-adjacent Example How to find the supplement of an angle Example 4: Find the complement of a 20° angle. Example 5: Supplementary Angles Algebra Application If the ratio of an angle to its supplement is 7 : 5 , find the measure of each angle. PERPENDICULAR LINES: lines, segments, or rays that form _________ angles. Lines / segments / rays are can be perpendicular Angles are NOT perpendicular Symbol: Example: PERPENDICULAR BISECTOR: a line or part of a line that is perpendicular to a segment and passes through the segment’s _________________. Forms _________ angles AND _______________ segments Example 6: Identifying angle pairs when given perpendicular lines. ⃡ , ⃡𝐆𝐉 ⊥ 𝐇𝐅 𝐚𝐭 𝐇 Refer to the figure to the right. 𝐃𝐄 G a) Name the right angles. F _____________________________ b) Name a pair of acute vertical angles. D E H _____________________________ c). Name a pair of obtuse vertical angles. J _____________________________ d). Name a pair of complementary angles. _____________________________ e) Name a linear pair. _____________________________ Example 8: Perpendicular Lines Algebra Application: ⃡. ⃡ ⊥ SQ Refer to the figure to the right. Find 𝑥 and 𝑦, so that PR x=________________ y=________________