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Lesson 3 RCSD Geometry Local MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:__________ U7 GEOMETRY Lesson 3: Solve for Unknown Angles—Transversals 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. New Vocabulary: A transversal is a line that intersects two or more lines (in the same plane). Remember that: - the word INTERIOR means BETWEEN the lines. - the word EXTERIOR means OUTSIDE the lines. - the word ALTERNATE means "alternating sides" of the transversal When the lines are NOT parallel When the lines are parallel... "Names" given to pairs of angles formed by two parallel lines cut by a transversal • alternate interior angles • corresponding angles • alternate exterior angles • same-side interior angles Alternate interior angles are "interior" (between the parallel lines), and they "alternate" sides of the transversal Identify the pairs of alternate interior angle __________________________ If two parallel lines are cut by a transversal, the alternate interior angles are congruent. Converse If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. RCSD Geometry Local MATHEMATICS CURRICULUM Lesson 3 Name:___________________________________ Period:________ Date:__________ U7 GEOMETRY Alternate exterior angles are "exterior" (outside the parallel lines), and they "alternate" sides of the transversal Identify all the pairs of alternate exterior angles ___________ _______________ If two parallel lines are cut by a transversal, the alternate exterior angles are congruent. Converse If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. If you copy one of the corresponding angles and you translate it along the transversal, it will coincide with the other corresponding angle. Identify all the pairs of coresponding angles __________________________ If two parallel lines are cut by a transversal, corresponding angles are congruent. Converse If two lines are cut by a transversal and corresponding angles are congruent, the lines are parallel. The "interior" angles same side (between the parallel lines), are on the same side of the transversal. Identify all the pairs __________________________ If two parallel lines are cut by a transversal, same-side interior angles are supplementary Converse If two lines are cut by a transversal and the same-side interior angles are supplementary, the lines are parallel Lesson 3 RCSD Geometry Local MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:__________ U7 GEOMETRY Using the theorems above, what equations can you create from the diagram at the right? Congruent: ______ = _____ Type: ________ Supplementary: ____ + ____ = ____ Type: ________ 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: ______ ______ Example 1 In the diagram below, find the unknown (labeled) angles. Give reasons for your solutions. 𝑚∠𝑎 = _______ Reason:________________________ 𝑚∠𝑏 = _______ Reason:________________________ 𝑚∠𝑐 = _______ Reason:________________________ Example 2 Given the diagram at the right with straight lines m, n and t. Which statement could always be used to prove 𝑚 || 𝑛 ? Choose: ∠2 and ∠6 are supplementary m∠2 = m∠3 ∠3 and ∠5 are supplementary m∠5 = m∠7 1. Lesson 3 RCSD Geometry Local MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:__________ U7 GEOMETRY Lesson 3: Solve for Unknown Angles—Transversals 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 ___________________________________ ____________________________________________________ RCSD Geometry Local MATHEMATICS CURRICULUM Lesson 3 Name:___________________________________ Period:________ Date:__________ In 4 and 5 , use the diagram at the right. 4. Given ∠2 ≅ ∠6, what justifies k || m. a. Converse Alternate Interior Angles Theorem b. Converse Alternate Exterior Angles Theorem c. Converse Corresponding Angles Theorem d. there is not enough info to state parallel 5. Given n || p , what justifies ∠1 ≅ ∠12 a. Alternate Interior Angles Theorem b. Alternate Exterior Angles Theorem c. Corresponding Angles Theorem d. there is not enough info to make this statement In 6 and 7, use the diagram at the right. 6. Determine the relationship between ∠1 & ∠10. a. Alternate Interior b. Same-side Interior c. Corresponding Angles d. None of these 7. Determine the relationship between ∠5 & ∠15. a. Alternate Exterior b. Alternate Interior c. Same-side Interior d. None of these 8. If m∠9 = 62°, then find the measure the following angles: a. m∠1= b. m∠2= c. m∠4= d. m∠5= e. m∠15= U7 GEOMETRY RCSD Geometry Local MATHEMATICS CURRICULUM Lesson 3 Name:___________________________________ Period:________ Date:__________ 9. Given straight lines p, q, t, and s and angles as marked. Which value of x will make lines p and q parallel? Choose: 73º 87º 107º 113º Given the diagram shown at the right. Assume all lines are straight. Find the measures of all of the numbered angles 1 through 12. m∠1 ________________ m∠2 ________________ m∠3 _________________ m∠4 _________________ m∠5 ________________ m∠6 _________________ m∠7 _________________ m∠8 _________________ m∠9 _________________ m∠10 _________________ m∠11 _________________ m∠12 _________________ U7 GEOMETRY Lesson 3 RCSD Geometry Local MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:__________ U7 GEOMETRY Lesson 3: Solve for Unknown Angles—Transversals Homework 1. Find the measure of the unknown angle, and give the name of the theorem used. A. B. ma = ________ mb = ________ Theorem: Theorem: ________________________ ____________________ __________________________________ C. ________________________________ D. mc = ________ md = ________ Theorem: Theorem: _______________________ ____________________ __________________________________ ________________________________ RCSD Geometry Local MATHEMATICS CURRICULUM Lesson 3 Name:___________________________________ Period:________ Date:__________ U7 GEOMETRY 2. 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 ________________. 3. Find the measures of all the angles given that 𝑙 ∥ 𝑚 . 𝑚∠𝑎 = _______ Reason:______________________ 𝑚∠𝑏 = _______ Reason:______________________ 𝑚∠𝑐 = _______ Reason:______________________