Lesson 7A: Solve for Unknown Angles Transversals
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1 Lesson 7A: Solve for Unknown Angles Transversals Warmup Directions: Solve any two out of three equations Check your answer: 1. 4(x 2) = 8(x 3) n = 8(3 + 4n) + 3n a + 5a = 3a 5a Challenge me 4. (x 1)(x + 5) = x 2 + 4x 2
2 Lesson 7A: Solve for Unknown Angles Transversals Mini-Lesson Learning Targets: I can identify all types of angles formed by parallel lines cut by transversal. I can apply the knowledge of relationships between angles formed by parallel lines cut by a transversal to find the missing angle. Using the theorems above, what equations can you create from the diagram at the right? Congruent: = Supplementary: + = Type: Type:
3 If we already know two lines are parallel, then we can say a. If two parallel lines are cut by a transversal, then the corresponding angles are. b. If two parallel lines are cut by a transversal, then the alternate interior angles are. c. If two parallel lines are cut by a transversal, then the same side interior angles are. Two lines AB and CD are parallel if and only if the following types of angle pairs are congruent or supplementary: Corresponding Angles are equal in measure. List all Corresponding angles: Alternate Interior Angles are equal in measure. List all pairs of Alternate Interior angles: Same Side Interior Angles are supplementary. List all pairs of Alternate Interior angles: Guided Practice: We do Example 1) In the diagram below, find the unknown (labeled) angles. Give reasons for your solutions. m a = m b = m c = Reason: Reason: Reason: Example 2) In the diagram at right, transversal TU intersects PQ and RS at V and W, respectively. If m TVQ = 5x 22 and m VWS = 3x 10, which value of x would result in PQ RS?
4 Lesson 7A M1 Classwork Two lines AB and CD are parallel if and only if any one of the following conditions are true: Corresponding Angles are equal in measure. or Alternate Interior Angles are equal in measure. or Same Side Interior Angles are supplementary: 1. Transversal intersects and, as shown in the diagram below. Which statement could always be used to prove? a) b) c) and are supplementary d) and are supplementary 2. A transversal intersects two lines. Which condition would always make the two lines parallel? a) Vertical angles are congruent. b) Alternate interior angles are congruent. c) Corresponding angles are supplementary. d) Same-side interior angles are complementary. 3. Find m 1 and then m 2. Justify each answer. m 1 because m 2 because
5 Lesson 7A M1 4. Find the value of x if and The diagram is not to scale l m 5. As shown in the diagram below, lines m and n are cut by transversal p. If m 1 = 4x + 14 and m 2 = 8x + 10, lines m and n are parallel when x equals 1) 1 2) 6 3) 13 4) In the diagram at right, line p intersects line m and line n. If m 1 = 7x and m 2 = 5x + 30, lines m and n are parallel when x equals 1) ) 15 3) ) 105
6 Homework 1. Find the measure of the unknown angle, and give the name of the theorem used. A. B. m a = m b = Theorem: Theorem: C. D. m c = m d = Theorem: Theorem: 2. Line n intersects lines l and m, forming the angles shown in the diagram at right. Which value of x would prove l m? 1) 2.5 2) 4.5 3) ) 8.75
7 3. Given that p q and l m, find the measures of all the numbered angles in the diagram, giving reasons for each measurement. The first one is done for you. a. m 1 = 42 by _corresponding angle theorem to Given Angle. b. m 2 = by to. c. m 3 = by to. d. m 4 = by to. e. m 5 = by to. f. m 6 = by to. g. m 7 = by to. h. m 8 = by to. 4. Lines p and q are intersected by line r, as shown at right. If m 1 = 7x 36 and m 2 = 5x + 12, for which value of x would q? 5. Peach Street and Cherry Street are parallel. Apple Street intersects them, as shown in the diagram at right. If m 1 = 2x + 36 and m 2 = 7x 9, what is m 1? 6. Find the measures of all the angles given that l m. m a = Reason: m b = Reason: m c = Reason:
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