Ch 7 Learning Goal: PLANE GEOMETRY Learn to describe the figures by using the terms of geometry (7-1) Learn to name, measure, classify, estimate and draw angles (7-2) Learn to understand relationship of angles (7-3) Learn to classify the different types of lines (7-4) Learn to classify triangles and solve problems involving angle and side measures of triangles (7-5) Learn to identify, classify, and compare quadrilaterals (7-6) Learn to identify regular and not regular polygons and to find the angle measures of regular polygons (7-7) Learn to recognize, describe, and extend geometric patterns (7-8) Learn to identify congruent figures and to use congruence to solve problems (7-9) Learn to use translations, reflections, and rotations to transform geometric shapes (7-10) Learn to identify line symmetry (7-11) Learn to identify tessellations and shapes that can tessellate (7-12)

Page 328 #11-27 Answers

6 th Grade Math Homework Page 334 #1-8

7-3 Angle Relationships Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up Identify the type of angle ° 2. 90° ° ° acute right obtuse Course Angle Relationships straight

Problem of the Day A line forms an angle of 57° with the vertical axis. What angle does the line form with the horizontal axis? 33° or 147° Course Angle Relationships

Today’s Learning Goal Assignment Learn to understand relationships of angles. Course Angle Relationships

Vocabulary congruent vertical angles adjacent angles complementary angles supplementary angles Insert Lesson Title Here Course Angle Relationships

Course Angle Relationships When angles have the same measure, they are said to be congruent. Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent. MRP and NRQ are vertical angles. MRN and PRQ are vertical angles MN 160° 20° R P Q

Course Angle Relationships Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent. MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ and QRP are adjacent angles. They share vertex R and RQ. MN 160° 20° R P Q

Course Angle Relationships 65° + 25° = 90° LMN and NMP are complementary. Complementary angles are two angles whose measures have a sum of 90°. P N M L 25° 65°

Course Angle Relationships Supplementary angles are two angles whose measures have a sum of 180°. 65° + 115° = 180° GHK and KHJ are supplementary. J K H 115°65° G

Math Internet Connect go.hrw.com Keyword: MR4 7-3

Online Practice Complete Z.6

Course Angle Relationships Additional Example 1A: Identifying Types of Angle Pairs Identify the type of each angle pair shown. A. 5 and 6 are opposite each other and are formed by two intersecting lines. They are vertical angles. 5 6

Course Angle Relationships Try This: Additional Example 1A Identify the type of each angle pair shown. A. 3 and 4 are side by side and have a common vertex and ray. They are adjacent angles. 3 4

Course Angle Relationships Additional Example 1B: Identifying Types of Angle Pairs Identify the type of each angle pair shown. B. 7 and 8 are side by side and have a common vertex and ray. They are adjacent angles. 7878

Course Angle Relationships Try This: Additional Example 1B Identify the type of each angle pair shown. B. 7 and 8 are opposite each other and are formed by two intersecting lines. They are vertical angles. 7 8

Course Angle Relationships Additional Example 1A: Identifying an Unknown Angle Measure Find each unknown angle measure. 71° + a = 90° –71° a = 19° The sum of the measures is 90°. a 71° A. The angles are complementary.

Course Angle Relationships Try This: Example 1A Find each unknown angle measure. 65° + d = 90° –65° d = 25° The sum of the measures is 90°. d 65° A. The angles are complementary.

Course Angle Relationships Additional Example 1B: Identifying an Unknown Angle Measure Find each unknown angle measure. 125° + b = 180° –125° b = 55° The sum of the measures is 180°. b 125° B. The angles are supplementary.

Course Angle Relationships Try This: Example 1B Find each unknown angle measure. 145° + s = 180° –145° s = 35° The sum of the measures is 180°. s 145° B. The angles are supplementary.

Course Angle Relationships Additional Example 1C: Identifying an Unknown Angle Measure Find each unknown angle measure. c = 82°Vertical angles are congruent. c 82° C. The angles are vertical angles.

Course Angle Relationships Try This: Example 1C Find each unknown angle measure. t = 32°Vertical angles are congruent. t 32° C. The angles are vertical angles.

Course Angle Relationships Additional Example 1D: Identifying an Unknown Angle Measure Find each unknown angle measure. x + y + 80° = 180° –80° x + y = 100° The sum of the measures is 180°. D. JKL and MKN are congruent. x = 50° and y = 50° Each angle measures half of 100°. x 80° K M L NJ y

Course Angle Relationships Try This: Example 1D Find each unknown angle measure. x + y + 50° = 180° –50° x + y = 130° The sum of the measures is 180°. D. ABC and DBE are congruent. x = 65° and y = 65° Each angle measures half of 130°. x 50° B DC EA y

Lesson Quiz Give the complement of each angle ° 2. 42° Give the supplement of each angle ° 4. 17° 5. Identify the type of angle pair shown. 48° 20° Insert Lesson Title Here 60°163° Course Angle Relationships adjacent