Building Blocks of Geometry Course 2 8-1 Building Blocks of Geometry 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

Building Blocks of Geometry Course 2 8-1 Building Blocks of Geometry 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;

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

Building Blocks of Geometry Course 2 8-1 Building Blocks of Geometry 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. Q R S A coordinate plane is an example of a plane. Helpful Hint

Additional Example 1: Identifying Points, Lines, and Planes Course 2 8-1 Building Blocks of Geometry 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

Insert Lesson Title Here Course 2 8-1 Building Blocks of Geometry 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

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

Additional Example 2: Identifying Line Segments and Rays Course 2 8-1 Building Blocks of Geometry 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

Building Blocks of Geometry Course 2 8-1 Building Blocks of Geometry 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 BA, CA, BD Use the endpoints in any order to name a segment.

Building Blocks of Geometry Course 2 8-1 Building Blocks of Geometry 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 A C 16 m

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

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

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

Course 2 8-2 Classifying Angles A C B 1 Vertex An angle is 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 (°).

8-2 Classifying Angles An angle’s measure determines the type of Course 2 8-2 Classifying Angles 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°. An obtuse angle is an angle that measures more than 90° but less than180°. A straight angle is an angle that measures 180°.

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

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

Insert Lesson Title Here Course 2 8-2 Classifying Angles 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

8-2 Classifying Angles If the sum of the measures of two angles is Course 2 8-2 Classifying Angles 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.

Course 2 8-2 Classifying Angles Additional Example 2A: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ 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 P Q R M Since 60° + 30° = 90°, PMQ and OMP are complementary.

Course 2 8-2 Classifying Angles 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. O N P Q R M Read mNMO as “the measure of angle NMO.” Reading Math

Course 2 8-2 Classifying Angles Additional Example 2C: Identifying Complementary and Supplementary Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. PMQ and QMR 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 P Q R M Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.

8-2 Classifying Angles Check It Out: Example 2A Course 2 8-2 Classifying Angles 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. C B D E F A

Additional Example 3: Finding Angle Measures Course 2 8-2 Classifying Angles 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. – 56° – 56° Subtract 56° from both sides to isolate mB. mB = 34° The measure of B = 34°.

8-2 Classifying Angles Check It Out: Example 3 Course 2 8-2 Classifying Angles 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. – 32° – 32° Subtract 32° from both sides to isolate mQ. mQ = 148° The measure of Q = 148°.

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

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