Geometric Relationships 5-1 Angle Relationships

Angle Review: What kind of angle is this? Right Angle 90⁰

Naming Angles Angles may be named by the vertex letter name Angle B Angles may be named using numbers Angle 1 Angles may be named using the vertex and points on each ray (vertex MUST be middle letter!) Angle ABC or Angle CBA A B 1 C

What kind of angle do the hands of a clock make at: 5:00? greater than 90⁰ obtuse 10:00? less than 90⁰ acute 3:00? exactly 90⁰ right

What kind of angle do the hands of a clock make at: 5:00? greater than 90⁰ obtuse 10:00? less than 90⁰ acute 3:00? exactly 90⁰ right 1:30? less than 90⁰ acute 8:30? greater than 90⁰ obtuse 6:00? greater than 90⁰ straight

Classifying Angles – Use the diagram to identify: C D 90⁰ 30⁰ 60⁰ A E B Two acute angles: 1) Angle AED or DEA 2) Angle CEB or BEC

Classifying Angles – Use the diagram to identify: C D 90⁰ 30⁰ 60⁰ A E B Two obtuse angles: 1) Angle AEC or CEA 2) Angle DEB or BED

Classifying Angles – Use the diagram to identify: C D 90⁰ 30⁰ 60⁰ A E B A pair of complementary angles: Angle AED and angle CEB = 90

Classifying Angles – Use the diagram to identify: C D 90⁰ 30⁰ 60⁰ A E B Two pairs of supplementary angles: 1) Angle AEC and angle CEB = 180 2) Angle AED and angle DEB = 180

Finding Angle Measures – Use the diagram to find each angle measure: If m ⁄ 2 = 75⁰, find m ⁄ 3. m ⁄ 2 + m ⁄ 3 = m ⁄ 3 = m ⁄ 3 = 105⁰ They form a straight line, so they are supplementary, which means they add up to 180⁰.

Finding Angle Measures – Use the diagram to find each angle measure: If m ⁄ 2 = 75⁰, find m ⁄ 4. ⁄ 2 and ⁄ 4 are vertical angles. m ⁄ 2 = 75⁰, so m ⁄ 4 = 75⁰ Vertical angles are congruent!

Art Application – An artist is designing a section of a stained glass window. Based on the diagram, what would be the measure of angle ECF? A B 32⁰ C D 32 E F 58⁰

Group Work Textbook page (1-8)

Homework Textbook page 199 (9-16)