Do Now What geometry term might you associate with each object? 1. one edge of a cardboard box

1. 8-1 Building Blocks of Geometry Course 2 Do Now What geometry term might you associate with each object? 1.one edge of a cardboard box 2. the floor 3. the tip of a pen line segment or line plane or rectangle point Hwk p 68 & 69 THIS SHOULD BE A REVIEW

2. 8-1 Building Blocks of Geometry Course 2 EQ: How do I identify / describe the building blocks of geometry and identify angles? M7P1.a Build new mathematical knowledge through problem solving; M7P1.b Solve problems that arise in mathematics and in other contexts;

3. Review %

4. 8-1 Building Blocks of Geometry XY, or YX Helpful Hint Use two points on the line to name a line. X Y A number line is an example of a line. Course 2 A point is an exact location in space. It is usually represented as a dot, but it has no size at all point A Use a capital letter to name a point. • A A lineis a straight path that extends without end in opposite directions.

5. 8-1 Building Blocks of Geometry Q S R Helpful Hint A coordinate plane is an example of a plane. Course 2 A plane is a perfectly flat surface that extends infinitely in all directions. plane QRS Use three points in any order, not on the same line, to name a plane.

6. 8-1 Building Blocks of Geometry Course 2 Additional Example 1: Identifying Points, Lines, and Planes Identify the figures in the diagram. D E F A. three points D, E, and F Choose any two points on a line to name the line. B. two lines DE, DF Choose any three points, not on the same line, in any order. C. a plane plane DEF

7. 8-1 Building Blocks of Geometry Course 2 Insert Lesson Title Here Check It Out: Example 1 Identify the figures in the diagram. G H I F A. four points H, G, I, and F Choose any two points on a line to name the line. B. two lines IH, HF Choose any three points, not on the same line, in any order. C. a plane plane IGF

8. 8-1 Building Blocks of Geometry GH Name the endpoint first when naming a ray. G H LM, or ML Use the endpoints to name a line segment. L M Course 2 A ray is a part of a line. It has one endpoint and extends without end in one direction. A line segmentis part of a line. or a ray that extends from one endpoint to another.

9. 8-1 Building Blocks of Geometry Course 2 Additional Example 2: Identifying Line Segments and Rays Identify the figures in the diagram. M N O A. three rays Name the endpoint of a ray first. MN, NM, MO B. two line segments Use the endpoints in any order to name a segment. MN, MO

10. 8-1 Building Blocks of Geometry Course 2 Check It Out: Example 2 Identify the figures in the diagram. D C A. three rays Name the endpoint of a ray first. B A BC, CA, BD B. three line segments Use the endpoints in any order to name a segment. BA, CA, BD

11. 8-1 Building Blocks of Geometry Course 2 Figures are congruent if they have the same shape and size. If you place one on top of the other, they match exactly. Line segments are congruent if they have the same length. You can use tick marks to indicate congruent line segments. In the illustration below, line segments AB and BC are congruent. B 20 m 20 m C A 16 m

12. 8-1 Building Blocks of Geometry A B AB CD E F ACBD C D BF DF EC AE Reading Math The symbol means “is congruent to.” Course 2 Additional Example 3: Identifying Congruent Line Segments Identify the line segments that are congruent in the figure. One tick mark Two tick marks Three tick marks

13. 8-1 Building Blocks of Geometry A AB AC BCDE B C BD CE E D Course 2 Insert Lesson Title Here Check It Out: Example 3 Identify the line segments that are congruent in the figure. One tick mark Two tick marks Three tick marks

14. 8-1 Building Blocks of Geometry AD, BE, CF Possible answer: GA, GB, GC Possible answer: AG, AD, DG, BG AG GD, GB GE Course 2 Insert Lesson Title Here You Try Identify the figures in the diagram. 1. lines 2. plane Possible answer: plane ABG 3. three rays 4. four line segments 5. Identify the line segments that are congruent in the figure.

15. 8-2 Classifying Angles A Vertex 1 B C Course 2 An angleis formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex. Angles are measured in degrees (°).

16. 8-2 Classifying Angles Course 2 An angle’s measure determines the type of angle it is. A right angle is an angle that that measures exactly 90°. The symbol indicates a right angle. An acute angle is an angle that measures less than 90°. Anobtuse angle is an angle that measures more than 90° but less than180°. A straightangle is an angle that measures 180°.

17. 8-2 Classifying Angles Course 2 Additional Example 1: Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. B. acute angle obtuse angle

18. 8-2 Classifying Angles A • 1 B• •C Reading Math You can name this angle ABC, CBA, B, or 1. Course 2

19. 8-2 Classifying Angles Course 2 Insert Lesson Title Here Check It Out: Example 1 Tell whether each angle is acute, right, obtuse, or straight. B. A. straight angle acute angle

20. 8-2 Classifying Angles Course 2 If the sum of the measures of two angles is 90°, then the angles are complementary angles. If the sum of the measures of two angles is 180°, then the angles are supplementary angles.

21. 8-2 Classifying Angles P Q To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mOMP = 60°. O N R M Course 2 Additional Example 2A: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ Since 60° + 30° = 90°, PMQ andOMP are complementary.

22. 8-2 Classifying Angles P Q O N R M Reading Math Read mNMO as “the measure of angle NMO.” Course 2 Additional Example 2B: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. NMO and OMR mNMO = 15° and mOMR = 165° Since 15° + 165° = 180°, NMO andOMR are supplementary.

23. 8-2 Classifying Angles P Q To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mQMR = 75°. O N R M Course 2 Additional Example 2C: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. PMQ and QMR Since 30° + 75° = 105°, PMQ andQMR are neither complementary or supplementary.

24. 8-2 Classifying Angles D E C F B A Course 2 Check It Out: Example 2A Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and CAF mBAC = 35° and mCAF = 145° Since 35° + 145° = 180°, BAC andCAF are supplementary.

25. 8-2 Classifying Angles Course 2 Additional Example 3: Finding Angle Measures Angles A and B are complementary. If mA is 56°, what is the mB? Since A and B are complementary, mA + mB = 90°. mA + mB = 90° 56° + mB = 90° Substitute 56° for mA. Subtract 56° from both sides to isolate mB. – 56° – 56° mB = 34° The measure of B = 34°.

26. 8-2 Classifying Angles Course 2 Check It Out: Example 3 Angles P and Q are supplementary. If mP is 32°, what is the mQ? Since P and Q are complementary, mP + mQ = 180°. mP + mQ = 180° 32° + mQ = 180° Substitute 32° for mP. Subtract 32° from both sides to isolate mQ. – 32°– 32° mQ = 148° The measure of Q = 148°.

27. 8-2 Classifying Angles 2. Course 2 Insert Lesson Title Here TOTD Tell whether each angle is acute, right, obtuse, or straight. straight 1. obtuse

28. 8-2 Classifying Angles Course 2 Insert Lesson Title Here TOTD Use the diagram to tell whether the angles are complementary, supplementary, or neither. 3. AZB and BZC neither complementary 4. BZC and CZD 5. Angles M and N are supplementary. If M is 117°, what is mN? 63°