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LESSON 3–1 Parallel Lines and Transversals Five-Minute Check (over Chapter 2) TEKS Then/Now New Vocabulary Key Concepts: Parallel and Skew Example 1: Real-World Example: Identify Parallel and Skew Relationships Key Concepts: Transversal Angle Pair Relationships Example 2: Classify Angle Pair Relationships Example 3: Identify Transversals and Classify Angle Pairs Over Chapter 2 Make a conjecture about the next number in the sequence, 5, 20, 80, 320. A. 380 B. 395 C. 1280 D. 1580 Over Chapter 2 Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts. A. If you do not live in Massachusetts, then you do not live in Boston. B. If you live in Massachusetts, then you do not live in Boston. C. If you do not live in Massachusetts, then you live in Boston. D. You might live in Massachusetts or Boston. Over Chapter 2 Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements. If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles. A. Yes, A and B are a linear pair. B. no conclusion Over Chapter 2 Name the property that justifies the statement. If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75. A. Substitution Property B. Reflexive Property C. Addition Property D. Symmetric Property Over Chapter 2 Find m1 and m2 if m1 = 8x + 18 and m2 = 16x – 6 and m1 and m2 are supplementary. A. m1 = 106, m2 = 74 B. m1 = 74, m2 = 106 C. m1 = 56, m2 = 124 D. m1 = 14, m2 = 166 Targeted TEKS G.5(A) Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools. Mathematical Processes G.1(E), G.1(F) You used angle and line segment relationships to prove theorems. • Identify relationships between two lines or two planes. • Name angle pairs formed by parallel lines and transversals. • parallel lines • skew lines • parallel planes • transversal • interior angles • exterior angles • consecutive interior angles • alternate interior angles • alternate exterior angles • corresponding angles Identify Parallel and Skew Relationships A. Name all segments parallel to BC. Answer: AD, EH, FG Identify Parallel and Skew Relationships B. Name a segment skew to EH. Answer: AB, CD, BG, or CF Identify Parallel and Skew Relationships C. Name a plane parallel to plane ABG. Answer: plane CDE A. Name a plane that is parallel to plane RST. A. plane WTZ B. plane SYZ C. plane WXY D. plane QRX B. Name a segment that intersects YZ. A. XY B. WX C. QW D. RS C. Name a segment that is parallel to RX. A. ZW B. TZ C. QR D. ST Transversal – a line that intersects two or more lines in a plane at different points. 1) Fold a third of a piece of copy paper down. Use a ruler, protractor, or straightedge to draw a straight line across the crease. 2) Draw this figure in the top third portion of the paper 1 3 5 6 7 8 2 4 Write the following information in the bottom section of your paper… Consecutive – same side of the transversal Alternate – opposite sides of the transversal Interior – in between the intersecting lines Exterior – outside of the intersecting lines Write the following information in the bottom section of your paper… Consecutive – same side of the transversal Alternate – opposite sides of the transversal Interior – in between the intersecting lines (Angles 3, 4, 5, and 6 are interior.) Exterior – outside of the intersecting lines (Angles 1, 2, 7, and 8 are exterior.) Write the following information in the bottom section of your paper… Corresponding – same side of the transversal and same side of the intersecting lines (could say same “corner” in the diagram) Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Corresponding Angles Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Corresponding Angles 1 and 5 2 and 6 3 and 7 4 and 8 Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Vertical Angles (congruent) Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Vertical Angles (congruent) 1 and 4 2 and 3 5 and 8 6 and 7 Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Alternate Exterior Angles Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Alternate Exterior Angles 1 and 8 2 and 7 Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Alternate Interior Angles Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Alternate Interior Angles 3 and 6 4 and 5 Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Consecutive Exterior Angles Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Consecutive Exterior Angles 1 and 7 2 and 8 Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Consecutive Interior Angles Write the following information in the bottom section of your paper… SPECIAL ANGLE RELATIONSHIPS Consecutive Interior Angles 3 and 5 4 and 6 Classify Angle Pair Relationships A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding Classify Angle Pair Relationships B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior Classify Angle Pair Relationships C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior Classify Angle Pair Relationships D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior A. Classify the relationship between 4 and 5. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior B. Classify the relationship between 7 and 9. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior C. Classify the relationship between 4 and 7. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior D. Classify the relationship between 2 and 11. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Identify Transversals and Classify Angle Pairs A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles. Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles. Identify Transversals and Classify Angle Pairs B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles. Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles. Identify Transversals and Classify Angle Pairs C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 4 and 5. Then classify the relationship between the pair of angles. Answer: The transversal connecting 4 and 5 is line y. These are consecutive interior angles. A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal. A. lines c, f B. lines c, d, e C. lines c, d, f D. lines c, d, e, f B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal. A. no lines B. lines c, f C. lines c, d, e, f D. lines a, c, d, e, f C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal. A. no lines B. lines a, b, d, e, f C. lines a, d, f D. lines a, b, e LESSON 3–1 Parallel Lines and Transversals CW – Transversals Pg. 176; #13-36