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Download Lesson 23: Base Angles of Isosceles Triangles Day 2
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Lesson 23 – Day 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ M1 GEOMETRY Lesson 23: Base Angles of Isosceles Triangles Day 2 Centers ̅̅̅̅ ∥ 𝑋𝑌 ̅̅̅̅̅is the angle bisector of ∠𝐵𝑌𝐴, and 𝐵𝐶 ̅̅̅̅. 1. Given: ∆𝐴𝐵𝐶, with 𝑋𝑌 Prove: 𝑌𝐵 = 𝑌𝐶. 2. 1.) 1.) Given 2.) 2.) Segment bisector divides segment into 2≅ segments 3.) 3.) Segment bisector divides segment into 2≅ segments 4.) 4.) Vertical <’s ≅ 5.) 5.) SAS NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ 3. 4. Given: 𝐴𝐵 = 𝐵𝐶, 𝐴𝐷 = 𝐷𝐶 Prove: ∆𝐴𝐷𝐵 and ∆𝐶𝐷𝐵 are right triangles Lesson 23 – Day 2 Period:________ Date:_________ M1 GEOMETRY Lesson 23 – Day 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ GEOMETRY Lesson 23: Base Angles of Isosceles Triangles Day 2 Homework 1. Given: ∆𝑅𝑆𝑇 is isosceles with 𝑅𝑆 = 𝑅𝑇, 𝑆𝑌 = 𝑇𝑍. Prove: ∆𝑅𝑆𝑌 ≅ ∆𝑅𝑇𝑍 2. ̅̅̅̅ Given: 𝐴𝐶 = 𝐴𝐸, ̅̅̅̅ 𝐵𝐹 ‖𝐶𝐸 Prove: 𝐴𝐵 = 𝐴𝐹 ̅̅̅̅ ≅ 𝑨𝑩 ̅̅̅̅. In your own words, describe how 3. In the diagram, ∆𝑨𝑩𝑪 is isosceles with 𝑨𝑪 transformations, and the properties of rigid motions, can be used to show that∠𝑪 ≅ ∠𝑩. (Use transparencies to identify the transformations) M1 Lesson 23 – Day 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ M1 GEOMETRY Teacher’s Prompts ̅̅̅̅ ∥ 𝑋𝑌 ̅̅̅̅̅is the angle bisector of ∠𝐵𝑌𝐴, and 𝐵𝐶 ̅̅̅̅. 1. Given: △ 𝐴𝐵𝐶, with 𝑋𝑌 Prove: 𝑌𝐵 = 𝑌𝐶. 1. ̅̅̅̅ 𝑩𝑪 ∥ ̅̅̅̅ 𝑿𝒀 1. Given 2. 𝒎∠𝑿𝒀𝑩 = 𝒎∠𝑪𝑩𝒀 2. Two ∥ lines are cut by a transversal, the alt. interior angles are =in measure 3. 𝒎∠𝑿𝒀𝑨 = 𝒎∠𝑩𝑪𝒀 3. Two ∥lines are cut by a transversal, the corresponding angles = in measure 4. 𝒎∠𝑿𝒀𝑨 = 𝒎∠𝑿𝒀𝑩 4. Definition of an angles bisector 5. 𝒎∠𝑪𝑩𝒀 = 𝒎∠𝑩𝑪𝒀 5. Substitution Property of Equality 6. 𝒀𝑩 = 𝒀𝑪 6. Base angles of a triangle are =, the triangle is isosceles( based on definition) 4. Given: 𝐴𝐵 = 𝐵𝐶, 𝐴𝐷 = 𝐷𝐶 Prove: ∆𝐴𝐷𝐵 and ∆𝐶𝐷𝐵 are right triangles m stands for measure 𝑨𝑩 = 𝑩𝑪 1. Given ∆𝑨𝑩𝑪 is isosceles 2. Definition of isosceles triangle 𝒎∠𝑨 = 𝒎∠𝑪 3. Base angles of an isosceles triangle are equal in m 𝑨𝑫 = 𝑫𝑪 4. Given ∆𝑨𝑫𝑩 ≅ ∆𝑪𝑫𝑩 𝒎∠𝑨𝑫𝑩 = 𝒎∠𝑪𝑫𝑩 ∠𝑨𝑫𝑩 + 𝒎∠𝑪𝑫𝑩 = 𝟏𝟖𝟎° 5. SAS 6 Corresponding angles of congruent triangles are = in m 7. Linear pairs form supplementary angles 𝟐(𝒎∠𝑨𝑫𝑩) = 𝟏𝟖𝟎° 8. Substitution Property of Equality 𝒎∠𝑨𝑫𝑩 = 𝟗𝟎° 9. Division Property of Equality 𝒎∠𝑪𝑫𝑩 = 𝟗𝟎° 10. Transitive Property ∆𝑨𝑫𝑩 and ∆𝑪𝑫𝑩 11. Definition of a right triangle are right triangles Lesson 23 – Day 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ Period:________ Date:_________ M1 GEOMETRY 3. 𝑾𝑴 = 𝑴𝑿 1. Definition of a midpoint 𝒎∠𝒁𝑾𝑴 = 𝟗𝟎° 2. Given 𝒎∠𝒀𝑿𝑴 = 𝟗𝟎° 𝟑. 𝑮𝒊𝒗𝒆𝒏 𝒎∠𝒁𝑾𝑴 = 𝒎∠𝒀𝑿𝑴 4. Transitive Property 𝑾𝒁 = 𝑿𝒀 5. Given/opposite sides on a rectangle are = ∆𝒁𝑾𝑴 ≅ ∆𝒀𝑿𝑴 6. SAS 𝒁𝑴 = 𝑴𝒀 ∆𝑨𝑫𝑩 is isosceles 7 Corresponding sides of congruent triangles are = 8. Definition of isosceles 2. 1.) 1.) Given 2.) 2.) Segment bisector divides segment into 2≅ segments 3.) 3.) Segment bisector divides segment into 2≅ segments 4.) 4.) Vertical <’s ≅ Lesson 23 – Day 2 NYS COMMON CORE MATHEMATICS CURRICULUM Name:___________________________________ 5.) Period:________ Date:_________ 5.) SAS M1 GEOMETRY
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