* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download of your Geometry Textbook
Survey
Document related concepts
Dessin d'enfant wikipedia , lookup
Euler angles wikipedia , lookup
Golden ratio wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Noether's theorem wikipedia , lookup
History of geometry wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Apollonian network wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Reuleaux triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Euclidean geometry wikipedia , lookup
Transcript
Name_________________________ Unit 4.1 – Triangles 1) Go to flippedmath.com Click here and select MyGeometry 2) Click on Semester 1 Unit 4 Open the MyGeometry course DoDEA Geometry Standard G.2: Triangles Students identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.) They prove that triangles are congruent or similar and use properties of these triangles to solve problems. G.1.1: Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning Section 4.1 Watch video entitled “Triangles” READ pages 218 - 220 and 250-252 of your Geometry Textbook The flippedmath.com video corresponds to the information presented in this section of your textbook. 3) HOMEWORK: Complete Unit 4.1 NO LATER THAN Dec 10 You have class time to complete the video, take notes, and start the practice and applications. There is also time for asking questions and clarifying concepts on an individual basis. USE THIS TIME WISELY TO BE SUCCESSFUL!!! Stay on task. REMEMBER: In addition to reading your text (pages 218-220 and 250252) you can open your online textbook and view the publisher’s lesson videos in your student resources E-mail if you have any questions: [email protected] 4.1 Triangles and Congruent Figures NOTES Write your questions here! ACUTE Types of triangles OBTUSE RIGHT SCALENE ISOSCELES EQUILATERAL Isosceles Triangle Theorem If… Then… Theorem If two sides of a triangle are congruent, then Theorem Converse of the Isosceles Triangle Theorem If… Then… If two angles of a triangle are congruent, then Write your questions here! Equilateral Triangle Theorem If… Then… Theorem If a triangle is equilateral, then Theorem Converse of the Equilateral Triangle Theorem If… Then… If a triangle is equiangular, then Congruent FiguresCorresponding PartsExample #1 Try it! Example #2 Summarize your notes: Now, summarize your notes here! 4.1 PRACTICE Draw the following. Mark the picture!!! 1. Obtuse Isosceles Triangle 2. Acute Equilateral Triangle 3. Right Scalene Triangle Find x. 4. 5. 6. 7. 8. 9. Mark the angles and sides of each pair of triangles to indicate that they are congruent. 10. 11. 12. Write a statement indicating that the triangle pair is congruent. ORDER IS IMPORTANT!!! 13. 14. 15. Complete each congruence statement. 16. 17. SOLVE 2(3𝑥 − 4) − 5 = −7 SOLVE 𝑥 𝑥+2 = 5 15 𝑦= 3 𝑥 4 18. ALGEBRA REVIEW GRAPH GRAPH 𝑦=𝑥 MULTIPLY (2𝑥 − 3)(𝑥 + 3) FACTOR 𝑥 − 4𝑥 − 12 2 4.1 APPLICATION 2. Given ∠𝑇 = 𝑥 2 and ∠𝐼 = 3𝑥 + 18. Find x. 1. Mark the picture. Watch the application walk through video if you need extra help getting started! In order to prove that two triangles are congruent, you must show that every corresponding angle and every corresponding side is congruent. 3. Mark the picture and then prove it. Show ALL SIDES and ALL ANGLES ≅ !!! ���� ∥ ���� Given: 𝑮𝑰 𝑻𝑹 ���� H is the midpoint of 𝑮𝑻 ���� ≅ 𝑹𝑻 ���� 𝑮𝑰 ����� ≅ ���� 𝑯𝑹 𝑰𝑯 Prove: ∆𝑮𝑯𝑰 ≅ ∆𝑻𝑯𝑹 STATEMENTS ��� ∥ 𝑇𝑅 ���� 1. 𝐺𝐼 ���� H is the midpoint of 𝐺𝑇 ��� ≅ ���� 𝐺𝐼 𝑅𝑇 ���� ��� 𝐻𝑅 ≅ �𝐼𝐻 REASONS 1. ���� ≅ 𝐻𝑇 ���� 2. 𝐺𝐻 2. 4. ∠𝐼 ≅ ∠𝑅 4. 3. ∠𝐺 ≅ ∠𝑇 3. Alternate Interior Angles are congruent 5. 5. 6. ∆𝐺𝐻𝐼 ≅ ∆𝑇𝐻𝑅 6. Definition of Congruent Triangles 4. Mark the picture and then prove it. Show ALL SIDES and ALL ANGLES ≅ !!! ����� Given: ∆𝑽𝑿𝑾 is an isosceles triangle with base 𝑽𝑾 ���� is an angle bisector of ∠𝑽𝑿𝑾 𝑿𝑷 ����� P is the midpoint of 𝑽𝑾 ∠𝑽𝑷𝑿 ≅ ∠𝑾𝑷𝑿 Prove: ∆𝑷𝑽𝑿 ≅ ∆𝑷𝑾𝑿 STATEMENTS 1. ∆𝑉𝑋𝑊 is an isosceles triangle ���� 𝑋𝑃 is an angle bisector of ∠𝑉𝑋𝑊 ����� P is the midpoint of 𝑉𝑊 ∠𝑉𝑃𝑋 ≅ ∠𝑊𝑃𝑋 REASONS 1. ���� ≅ 𝑋𝑃 ���� 2. 𝑋𝑃 2. ���� ≅ 𝑋𝑊 ����� 3. 𝑉𝑋 3. 4. 4. 5. ∠𝑉𝑋𝑃 ≅ ∠𝑊𝑋𝑃 5. 7. ∆𝑃𝑉𝑋 ≅ ∆𝑃𝑊𝑋 7. 6. ∠𝑋𝑉𝑃 ≅ ∠𝑋𝑊𝑃 6. 5. Fill in the measure of every angle: GIVEN: Name any isosceles triangles.