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Analytic Geometry Unit 1: Similarity, Congruence & ProofsNameTopic: Reasoning in Algebra and GeometryLesson 1Date PeriodClass Website: msgiwa1.weebly.com
NameClassDateAnalytic Geometry Unit 1: Similarity, Congruence & ProofsLesson 1PracticeForm GReasoning in Algebra and GeometryFill in the reason that justifies each step.1. 0.25x 2x 12 39Givena. ?2.25x 12 392.25x 27b.?225x 2700c.?d.?x 122. Given: m ABC 80m ABD m DBC m ABC(3x 3) (6x 5) 80Angle Addition PostulateASubstitution Property9x 8 80a.?9x 72b.?x 8c.?(3x 3) (6x 5) B3. Given: KL 3(PM)DC5x5x 3(2x - 4)Substitution Property K5x 6x - 12a.?-x -12b.?x 12c.?L2x 4PM6m 178m 54. Given: XY YZ8m 5 6m 17Substitution Property2m 5 17a.?2m 12b.?m 6c.?XYZName the property of equality or congruence that justifies going from the firststatement to the second statement.5. XY TZ6. 3(x 2) 15TZ XY3x 6 157. 4n 6 - 2n 92n 6 9Topic: Complementary8. A B and B C A CCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.and Supplementary Angles
Analytic Geometry Unit 1: Similarity, Congruence & ProofsLesson 1TYPES OF ANGLES:1. Acute: Acute angles have measures between and .Sketch:2. Right: A right angle has measure equal to .3. Obtuse: Obtuse angles have measures between and .SPECIAL PAIRS OF ANGLES:4. Complementary Angles: Pair of angles whose sum of measures equals .40 and 50 angles are complementary angles because 40 50 90 .Example: A 40 angle is called the complement of the 50 angle.Similarly, the 50 angle is the complement of the 40 angle.Practice: Find the complement of each angle.a) 35 b) 48 c) 12 5. Supplementary Angles: Pair of angles whose sum of measures equals .60 and 120 angles are supplementary angles because 60 120 180 .Example: A 60 angle is called the supplement of the 120 angle.Similarly, the 120 angle is the supplement of the 60 angle.Practice: Find the supplement of each angle.a) 40 b) 126 c) 72 1. Angle Bisector: A ray (or line or segment) that divides an angle into two(two angles with equal measure).Topic: Vertical Angles and Linear PairsIf two angles share a and together they make a , then the two anglesare called a linear pair.
NameClassDateAnalytic Geometry Unit 1: Similarity, Congruence & ProofsPracticeForm KProving Angles CongruentFind the value of each variable.To start, identify the relationship between the markedangles in the diagram.The marked angles are ? .1.(68 x) 3x Then write an equation to express this relationship.? ?2.Lesson 13.(10x 18) y (3x 10) y (4x 40) (8x 14) Find the measures of the labeled angles in each exercise.4. Exercise 15. Exercise 26. Exercise 3Developing Proof Complete the following proofby filling in the blanks.7. Given: 1 234Prove: 3 4Statements1 52Reasons1) 1 21) Given2) m 1 m 3 m 5 1802) ?3) m 1 m 3 90 1803) ?4) m 1 m 3 904) ?5) m 4 m 2 m 55) ?6) m 4 m 2 906) ?7) m 4 m 1 907) ?8) m 4 m 38) ?8. Reasoning A and B are adjacent complementary angles. C issupplementary to the angle formed by A and B. What can youconclude about C? Explain.Copyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.
NameClassDateAnalytic Geometry Unit 1: Similarity, Congruence & ProofsLesson 1Practice (continued)Form KProving Angles Congruent9. Developing Proof Fill in the blanks tocomplete the paragraph proof below.4Given: 1 43 2Prove: 2 31 1 4 because it is given. 1 2 by the ? . 2 4 by the ? . 3 4 by the ? . It follows that ? ? by the ? .Algebra Find the value of each variable and the measure of each labeled angle.10.11.(5x 8) (9x 2) (3x 10) (10x 2) (10x 12) Name two pairs of congruent angles in each figure. Justify your answers.Z12.QW13.XYAEGHCFBAlgebra Find the measure of each angle.14. A is three times as large as its complement, B.15. A is 21 less than twice as large as its supplement, B.16. A is congruent to its supplement, B.17. A is 18 more than five times its complement, B.Copyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.D
Analytic Geometry Unit 1: Similarity, Congruence & Proofs Lesson 1 Name _ Date _ Period _ Topic: Reasoning in Algebra and Geometry Class Website . Practice: Find the complement of each angle. a) 35 b) 48 c) 12 5.
