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# Download Lesson 7A: Solve for Unknown Angles—Transversals

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Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Name:___________________________________ Period:________ Date:__________ Lesson 7A: Solve for Unknown AnglesβTransversals Warmup Directions: Solve any two out of three equations Check your answer: 1. 4(π₯ β 2) = 8(π₯ β 3) β 12 2. 39 β 8π = β8(3 + 4π) + 3π 3. β7 β 6π + 5π = 3π β 5π Challenge me ο 4. (π₯ β 1)(π₯ + 5) = π₯ 2 + 4π₯ β 2 Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Name:___________________________________ Period:________ Date:__________ Lesson 8: Solve for Unknown AnglesβTransversals 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: ______ = _____ Type: ________ Supplementary: ____ + ____ = ____ Type: ________ Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Name:___________________________________ Period:________ Date:__________ If we already know two lines are parallel, then we can sayβ¦ a. βIf two parallel lines are cut by a transversal, then the corresponding angles are ____________________.β b. βIf two parallel lines are cut by a transversal, then the alternate interior angles are _____________________.β c. βIf two parallel lines are cut by a transversal, then the same side interior angles are____________________.β Two lines π΄π΅ and πΆπ· 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. πβ π = _______ Reason:________________________ πβ π = _______ Reason:________________________ πβ π = _______ Reason:________________________ Example 2) In the diagram at right, transversal β‘ππ intersects β‘ππ and β‘π π at V and W, respectively. If πβ πππ = 5π₯ β 22 and πβ πππ = 3π₯ β 10 , which value of x would result in β‘ππ β₯ β‘π π ? Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Name:___________________________________ Period:________ Date:__________ Lesson 8: Solve for Unknown AnglesβTransversals Classwork Two lines π΄π΅ and πΆπ· are parallel if and only if any one of the following conditions are true: ο· Corresponding Angles are equal in measure. or ο· Alternate Interior Angles are equal in measure. or ο· 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 β 1 and then mβ 2. Justify each answer. m ο1 ο½ __________because __________________________________ ____________________________________________________ m ο2 ο½ _________because ___________________________________ ____________________________________________________ Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Name:___________________________________ 4. Find the value of x if not to scale. and Period:________ Date:__________ The diagram is 1 2 3 l 4 5 6 7 5. As shown in the diagram below, lines m and n are cut by transversal p. If πβ 1 = 4π₯ + 14 and πβ 2 = 8π₯ + 10 , lines m and n are parallel when x equals 1) 1 2) 6 3) 13 4) 17 6. In the diagram at right, line p intersects line m and line n. If πβ 1 = 7π₯ and πβ 2 = 5π₯ + 30, lines m and n are parallel when π₯ equals 1) 12.5 2) 15 3) 87.5 4) 105 8 m Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Name:___________________________________ Period:________ Date:__________ Lesson 8: Solve for Unknown AnglesβTransversals Homework 1. Find the measure of the unknown angle, and give the name of the theorem used. A. B. mοa = ________ mοb = ________ Theorem: ____________________ Theorem: ________________________ __________________________________ ________________________________ C. D. mοc = ________ mοd = ________ 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 π β₯ π ? 1) 2.5 2) 4.5 3) 6.25 4) 8.75 3. Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Name:___________________________________ Period:________ Date:__________ 4. Given that π β₯ π and π β₯ π , find the measures of all the numbered angles in the diagram, giving reasons for each measurement. The first one is done for you. a. b. c. d. e. f. g. h. πβ 1 = πβ 2 = πβ 3 = πβ 4 = πβ 5 = πβ 6 = πβ 7 = πβ 8 = 42 _____ _____ _____ _____ _____ _____ _____ by _corresponding angle theorem__ to __Given Angle___. by ______________________________ to ________________. by ______________________________ to ________________. by ______________________________ to ________________. by ______________________________ to ________________. by ______________________________ to ________________. by ______________________________ to ________________. by ______________________________ to ________________. 5. Lines p and q are intersected by line r, as shown at right. If πβ 1 = 7π₯ β 36 and πβ 2 = 5π₯ + 12 , for which value of x would π β₯ π ? 6. Peach Street and Cherry Street are parallel. Apple Street intersects them, as shown in the diagram at right. If πβ 1 = 2π₯ + 36 and πβ 2 = 7π₯ β 9 , what is πβ 1 ? 7. Find the measures of all the angles given that π β₯ π . πβ π = _______ Reason:______________________ πβ π = _______ Reason:______________________ πβ π = _______ Reason:______________________