ACA Geometry Unit 2 Part 2 packet.pdf

Name: ________________________________________________ Unit 2 Part 2: Slope, transversals & Angle relationships  Slope Review Slope from a Graph Slope from a Table Slope from two points (make a table) Slope from two...

Name: ________________________________________________ Unit 2 Part 2: Slope, transversals & Angle relationships  Slope Review Slope from a Graph Slope from a Table Slope from two points (make a table) Slope from two points (Slope Formula)  Parallel and Perpendicular Lines & Slope Intercept Form Slope: Slope: Parallel: Parallel: Perpendicular: Perpendicular:  Slope-Intercept & Point-Slope Form Slope-Intercept Form Slope: y-intercept: Slope-intercept Form: Slope: y-intercept: Point-Slope Form Slope=______ Slope-intercept Form: Point-slope Form: Slope=______ Slope=______ Slope-intercept Form Slope-intercept Form: Point-slope Form: Point-slope Form:  Standard Form Review Converting Standard Form to Slope-intercept Form Convert each Standard Form equation to Slope-intercept Form to match the equation to the graph. Graph: Graph: Graph: Using Graph A, create an Using Graph B, create an Using Graph C, create an equation for each line then graph equation for each line then graph equation for each line then graph it. it. it. 1. Parallel Line 1. Parallel Line 1. Parallel Line 2. Perpendicular Line 2. Perpendicular Line 2. Perpendicular Line Day 6: Intro to angles and angle relationships Name: Date: ___________________________________________________ ________________________________ Topic: Class: ___________________________________________________ ________________________________ Main Ideas/Questions Notes An angle is formed by two ____________ with a common endpoint. Angles This common endpoint is called the ________________ The rays are called the ______________. A Name an angle using _____________ letters. The middle letter must always represent the vertex! 60° Use a single letter if there is only one angle located at the vertex. B C When referring to the measure of an angle, use a lowercase m. Example: mABC = 60° Types of Angles Example 1 a) Name the vertex of the angle. ______________ b) Name the sides of the angle. __________________ K L c) Give three ways to name the angle. _________________, _________________, _________________ J d) Classify the angle. _________________ Example 2 a) Name the vertex of the angle. ______________ b) Name the sides of the angle. __________________ c) Give three ways to name the angle. R T _________________, _________________, _________________ S d) Classify the angle. _________________ Congruent If _______________________, then the angles are 75° congruent. This is written as _________________. Angles A 75° B © Gina Wilson (All Things Algebra®, LLC), 2014-2019  VERTICAL ANGLES Two angles across from each other on intersecting lines. They are always congruent! Example: ADJACENT LINEAR PAIR ANGLES Two angles that are adjacent and supplementary. Two angles that are They form a straight line! next to each other and share a common side. Example: ANGLE Example: Relationships COMPLEMENTARY SUPPLEMENTARY ANGLES ANGLES Any two angles whose sum is 90° Any two angles whose sum is 180° Example: Example: © Gina Wilson (All Things Algebra®, LLC), 2014-2019 Identifying Types of Angles: Check all relationships between 1 and 2. 1 2  Adjacent  Adjacent 1  Vertical  Vertical 1  Complementary  Complementary 2 2  Supplementary  Supplementary  Linear Pair  Linear Pair 3 4  Adjacent  Adjacent  Vertical  Vertical 1  Complementary 1  Complementary 2 2  Supplementary  Supplementary  Linear Pair  Linear Pair 5 6  Adjacent  Adjacent 1  Vertical 1  Vertical  Complementary  Complementary  Supplementary 2  Supplementary 2  Linear Pair  Linear Pair © Gina Wilson (All Things Algebra®, LLC), 2014-2019  Using ANGLE RELATIONSHIPS to find ANGLE MEASURES Directions: Find the missing measures in each figure. Keep the angle relationships in mind. 1. 2. 3. 112° x° x° 68° 124° x° 4. 5. y° x° y° x° ° z 43° 72° z° 6. 1 and 2 are vertical angles. If the 7. A and B are complementary angles. If measure of 2 is 105°, find the measure of the measure of A is 42°, find the measure 1. of B. 8. P and Q are supplementary angles. If 9. 1 and 2 form a linear pair. If the the measure of Q is 64°, find the measure measure of 1 is 113°, find the measure of of P. 2. USING ALGEBRA 10. If mPQT = (3x + 47)° and mSQR = (6x – 25)°, find the measure of SQR. P T Q S R 11. If AB  CD , mDCE = (7x + 2)° and mECB = (x + 8)°, find the measure of DCE. D E A C B 12. If mKNM = (8x – 5)° and mMNJ = (4x – 19)°, find the measure of KNM. L K N J M © Gina Wilson (All Things Algebra®, LLC), 2014-2019 13. If mDEG = (5x – 4)°, mGEF = (7x – 8)°, mDEH = (9y + 5)°, find the values of x and y. F G E D H 14. R and S are complementary angles. If 15. P and Q are supplementary angles. If mR = (12x – 3)° and mS = (7x – 2)°, find mP = (4x + 1)° and mQ = (9x – 3)°, find mR. mQ. 16. 1 and 2 form a linear pair. The 17. J and K are complementary angles. measure of 2 is six more than twice the The measure of J is 18 less than the measure of 1. Find m2. measure of K. Find the measure of each angle. 18. If UW bisects TUV, mTUW = (13x – 5)° and mWUV = (7x + 31)°, find the value of x. U T V W 19. If MO bisects PMN, mPMN = 74° and mOMN = (2x + 7)°, find the value of x. P O L M N 20. If EF bisects CEB, mCEF = (7x + 21)° and mFEB = (10x – 3)°, find the measure of DEB. C F A E D B © Gina Wilson (All Things Algebra®, LLC), 2014-2019 Name: ___________________________________ Unit 1: Geometry Basics Date: __________________________ Per: ______ Homework 6: Angle Relationships ** This is a 2-page document! ** 1. Find the missing measure. 2. Find the missing measure. 3. Find the missing measures. x° 65° 51° x° x ° 107° z° y° 4. If the measure of an angle is 13°, find the 5. If the measure of an angle is 38°, find the measure of its supplement. measure of its complement. 6. 1 and 2 form a linear pair. If m1 = (5x + 9)° and m2 = (3x + 11)°, find the measure of each angle. 7. 1 and 2 are vertical angles. If m1 = (17x + 1)° and m2 = (20x – 14)°, find m2. 8. K and L are complementary angles. If mK = (3x + 3)° and mL = (10x – 4)°, find the measure of each angle. 9. If mP is three less than twice the measure of Q, and P and Q are supplementary angles, find each angle measure. 10. If mB is two more than three times the measure of C, and B and C are complementary angles, find each angle measure. © Gina Wilson (All Things Algebra®, LLC), 2014-2017 11. Find the value of x. 12. Find the value of x. (11x – 15)° (6x + 7)° (8x – 17)° (5x – 13)° 13. If BD  AC , mDBE = (2x – 1)°, and 14. Find the value of x if QS bisects PQR and mCBE = (5x – 42)°, find the value of x. mPQR = 82°. A P (10x + 1)° B D S Q C E R 15. Find the values of x and y. (10x – 61)° (18y + 5)° (x + 10)° 16. Find the values of x and y. (2y + 5)° (5x – 17)° (3x – 11)° 17. If NP bisects MNQ, mMNQ = (8x + 12)°, mPNQ = 78°, and mRNM = (3y – 9)°, find the values of x and y. R O O N M Q P O O © Gina Wilson (All Things Algebra®, LLC), 2014-2017  t l A line that intersects two or more lines. TRANSVERSAL m Example: ____________________________ AnGlEs formed by TrAnSvErSaLs Diagram Angle Pairs Examples _____________, _____________, Corresponding Angles (Angles on the same side of the transversal and in the same position.) _____________, _____________ t l Alternate Interior Angles ______________, 1 2 4 3 (Interior angles, non-adjacent, and on opposite sides of the transversal.) ______________ 5 6 8 7 m ______________, Alternate Exterior Angles (Exterior angles, non-adjacent, and on opposite sides of the transversal.) ______________ Consecutive Interior Angles ______________, (Interior angles that are on the same side of the transversal.) ______________ Examples! Name the type of angle relationship. If no relationship, write “none.” 1 a. ∠1 and ∠8 b. ∠2 and ∠3 1 2 c. ∠5 and ∠7 3 4 5 6 r 7 8 d. ∠2 and ∠7 q e. ∠1 and ∠3 p f. ∠6 and ∠7 2 a. ∠5 and ∠13 5 6 b. ∠7 and ∠14 1 2 7 8 3 4 c. ∠3 and ∠6 9 10 13 14 d d. ∠9 and ∠16 11 12 15 16 e. ∠4 and ∠7 a b f. ∠2 and ∠10 g. ∠8 and ∠14 Important! Angles must belong to h. ∠6 and ∠11 the SAME transversal to i. ∠4 and ∠13 be an angle pair. j. ∠4 and ∠9 © Gina Wilson (All Things Algebra), 2014  AnGlEs formed by TrAnSvErSaLs 5 7 j Name that Transversal! 1 3 6 8 ∠1 and ∠12: _______________ 2 4 ∠3 and ∠6: _______________ 9 11 13 15 ∠7 and ∠15: _______________ 10 12 14 16 k ∠12 and ∠14: ______________ l m Corresponding Alternate Interior Alternate Exterior Consecutive Interior Angles Angles Angles Angles _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ _______________________ Non- Non-Examples: © Gina Wilson (All Things Algebra), 2014 5. Using the diagram below, classify the angle pairs as corresponding, alternate interior, alternate exterior, consecutive interior, or none. 5 6 r 1 2 13 14 9 10 3 4 7 8 s 11 12 15 16 p q a. ∠4 and ∠7 b. ∠2 and ∠11 c. ∠12 and ∠16 d. ∠8 and ∠13 e. ∠11 and ∠15 f. ∠7 and ∠10 g. ∠1 and ∠14 h. ∠12 and ∠15 i. ∠6 and ∠7 j. ∠1 and ∠3 k. ∠12 and ∠16 l. ∠6 and ∠15 m. ∠5 and ∠10 n. ∠8 and ∠14 © Gina Wilson (All Things Algebra), 2014  Parallel Lines & Transversals If two PARALLEL lines are cut by a transversal, then… Each pair of corresponding angles is congruent Each pair of alternate interior angles is congruent. Each pair of alternate exterior angles is congruent. Each pair of consecutive interior angles is supplementary. And recall from Unit 1, vertical angles are always congruent and a linear pair is always supplementary. {So if we know one angle measure, then we can find them all!} Example 1 Given m∠1 = 65°, find the measure of each missing angle. Give your reasoning. 1 2 a. m∠2 = 4 3 5 6 b. m∠3 = 8 7 c. m∠4 = d. m∠5 = e. m∠6 = f. m∠7 = g. m∠8 = Example 2 Given m∠6 = 142°, find the measure of each missing angle. Give your reasoning. a. m∠1 = 5 1 b. m∠2 = 6 2 c. m∠3 = 7 3 8 d. m∠4 = 4 e. m∠5 = f. m∠7 = g. m∠8 = © Gina Wilson (All Things Algebra), 2014 Example 3 Given m∠5 = 82°, find the measure of each missing angle. a. m∠1 = e. m∠6 = i. m∠10 = 1 7 2 8 3 9 b. m∠2 = f. m∠7 = j. m∠11 = 4 10 5 11 6 12 c. m∠3 = g. m∠8 = k. m∠12 = d. m∠4 = h. m∠9 = Example 4 Given m∠12 = 121° and m∠ 6 = 75°, find the measure of each missing angle. 2 a. m∠1 = e. m∠5 = i. m∠10 = 1 3 4 5 6 b. m∠2 = f. m∠7 = j. m∠11 = 7 8 9 10 c. m∠3 = g. m∠8 = k. m∠13 = 11 12 13 14 d. m∠4 = h. m∠9 = l. m∠14 = Example 5 Given m∠7 = 38° and m∠10 = 102°, find the measure of each missing angle. a. m∠1 = f. m∠6 = k. m∠13 = 9 10 1 2 b. m∠2 = g. m∠8 = l. m∠14 = 12 11 4 3 5 6 c. m∠3 = h. m∠9 = m. m∠15 = 13 14 8 7 16 15 d. m∠4 = i. m∠11 = n. m∠16 = e. m∠5 = j. m∠12 = Example 6 Given m∠2 = 41°, m∠5 = 94°, and m∠ 10 = 109°, find the measure of each missing angle. 1 6 2 7 a. m∠1 = d. m∠6 = g. m∠9 = 3 b. m∠3 = e. m∠7 = 8 4 9 c. m∠4 = f. m∠8 = 5 10 © Gina Wilson (All Things Algebra), 2014  Parallel Lines, Transversals, and Algebra! Directions: If l l l m, find the value of each missing variable(s). 1. 2. 58° (16x + 22)° l l (5x – 2)° m m l 134° l 3. 4. (7x – 1)° (9x + 2)° 133° 125° m l l l m 5. l 6. (8x – 77)° (11x – 47)° l m (3x + 38)° (6x – 2)° m 7. 8. l l (13x – 21)° (5x + 3)° (5x + 75)° (9x – 33)° m m l 9. l (8x – 31)° (5y + 35)° (6x + 3)° m l 10. (29x – 3)° (13y – 17)° (15x + 7)° m l © Gina Wilson (All Things Algebra), 2014 11. l m l 12. (9x – 2)° (10y + 6)° (5x + 54)° l m l 13. l m l 14. Note: j l l k and l l l m (15y – 48)° j (8x – 1)° (11x – 25)° k l l m c m 15. 39° (4x + 4)° l c m (7x – 44)° (8y – 43)° m 16. (15x – 26)° (12x + 1)° 28° (4y – 9)° l m © Gina Wilson (All Things Algebra), 2014