Parallel Lines and Transversals LESSON 31 Lesson Menu 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 5-Minute Check 1 A.380 B.395 C.1280 D.1580 Make a conjecture about the next number in the sequence, 5, 20, 80, 320. Over Chapter 2 5-Minute Check 2 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. Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts. Over Chapter 2 5-Minute Check 3 A.Yes, A and B are a linear pair. B.no conclusion 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. Over Chapter 2 5-Minute Check 4 A.Substitution Property B.Reflexive Property C.Addition Property D.Symmetric Property Name the property that justifies the statement. If m 1 + m 2 = 75 and m 2 = m 3, then m 1 + m 3 = 75. Over Chapter 2 5-Minute Check 5 A.m 1 = 106, m 2 = 74 B.m 1 = 74, m 2 = 106 C.m 1 = 56, m 2 = 124 D.m 1 = 14, m 2 = 166 Find m 1 and m 2 if m 1 = 8x + 18 and m 2 = 16x 6 and m 1 and m 2 are supplementary. Over Chapter 2 5-Minute Check 6 A.24 B.42 C.68 D.84 The measures of two complementary angles are x + 54 and 2x. What is the measure of the smaller angle? TEKS 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) Then/Now 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. Vocabulary parallel lines skew lines parallel planes transversal interior angles exterior angles consecutive interior angles alternate interior angles alternate exterior angles corresponding angles Concept Example 1 Identify Parallel and Skew Relationships Answer: AD, EH, FG A. Name all segments parallel to BC. Example 1 Identify Parallel and Skew Relationships B. Name a segment skew to EH. Answer: AB, CD, BG, or CF C. Name a plane parallel to plane ABG. Example 1 Identify Parallel and Skew Relationships Answer: plane CDE Example 1a A.plane WTZ B.plane SYZ C.plane WXY D.plane QRX A.Name a plane that is parallel to plane RST. Example 1b B.Name a segment that intersects YZ. A.XY B.WX C.QW D.RS Example 1c C.Name a segment that is parallel to RX. A.ZW B.TZ C.QR D.ST Concept Example 2 Classify Angle Pair Relationships A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding Example 2 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 Example 2 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 Example 2 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 Example 2a A.alternate interior B.alternate exterior C.corresponding D.consecutive interior A. Classify the relationship between 4 and 5. Example 2b A.alternate interior B.alternate exterior C.corresponding D.consecutive interior B. Classify the relationship between 7 and 9. Example 2c A.alternate interior B.alternate exterior C.corresponding D.consecutive interior C. Classify the relationship between 4 and 7. Example 2d A.alternate interior B.alternate exterior C.corresponding D.consecutive interior D. Classify the relationship between 2 and 11. Example 3 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. Example 3 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. Example 3 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. Example 3a A.lines c, f B.lines c, d, e C.lines c, d, f D.lines c, d, e, f A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal. Example 3b A.no lines B.lines c, f C.lines c, d, e, f D.lines a, 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. Example 3c A.no lines B.lines a, b, d, e, f C.lines a, d, f D.lines a, b, e C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal. Parallel Lines and Transversals LESSON 31