Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Technical drawing wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Line (geometry) wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Trigonometric functions wikipedia , lookup
Foundations of Math 2 Final Exam Review Name: ______________________________________ UNIT 4: GEOMETRY, ANGLES, AND SIMILAR TRIANGLES Part 1: Vocabulary Congruent – Exactly the ______________________ Midpoint – The _______________________ of a segment Bisector – Cuts a segment or angle in ______________ Parallel – 2 lines that never ________________ Perpendicular – 2 lines that intersect at a _______________________ Transversal – a line that intersects 2 ___________________ Complementary Angles – 2 or more angles that add up to _________ Supplementary Angles – 2 or more angles that add up to ________ Linear Pair – 2 angles that are ________________ and add up to 180° Vertical Angles – 2 angles that are formed by an X. They are the angles that are ________________ from each other __________________________________________________________________________________________ Part 2: Angle Pair Relationships Corresponding Angles ___________________________________________ ___________________________________________ ___________________________________________ 1 and 5 2 and 6 3 and 7 4 and 8 Alternate Exterior Angles ___________________________________________ ___________________________________________ ___________________________________________ 1 and 7 2 and 8 Unit 8: Page 1 of 3 Alternate Interior Angles __________________________________________ __________________________________________ __________________________________________ 3 and 6 4 and 5 Consecutive Interior Angles __________________________________________ __________________________________________ __________________________________________ 3 and 5 4 and 6 Use the picture to determine if the angles are Supplementary, Vertical, Corresponding, Alternate Interior, Alternate Exterior, Consecutive, or No Relationship 1. Angles 1 and 3: _______________________ 2. Angles 3 and 5: _______________________ 3. Angles 2 and 8: _______________________ 4. Angles 1 and 6: _______________________ 5. Angles 4 and 5: _______________________ 6. Angles 5 and 6: _______________________ If 2 lines are parallel, Vertical Angles are ________________________ Corresponding Angles are ________________________ Alternate Interior Angles are ________________________ Alternate Exterior Angles are ________________________ Consecutive Angles are ________________________ which means, add up the angles and set them equal to __________ Now try these: 1. 2. X = ______________ X = ______________ Part 3: Triangle Sum Theorem The 3 angles in a triangle always _________________________________ Example: Now you try: 1. 2. X = __________ X = __________ Unit 8: Page 2 of 3 X = __________ Part 4: Similar Triangles There are 3 ways to prove that triangles are similar 1. ___________________________ (AA) – Prove that 2 angles are _____________________ 2. ___________________________ (SAS) – Prove the 2 sides and _____________________and 1 angle is _____________________ 3. ___________________________ (SSS) – Prove that all 3 sides are _____________________ Example 1. The triangles share an ANGLE at the top of the triangles 2. Set up the proportions 𝟏𝟎 𝟓 = 𝟖 𝟒 The proportions are equal! THE TRIANGLES ARE SIMILAR BY SAS and ∆𝑸𝑹𝑺~∆𝑸𝑻𝑾 You Try 1. 2. Reason: ____________ Reason: _____________ ∆𝑫𝑨𝑹~∆______________ ∆𝑨𝑩𝑪~∆_______________ __________________________________________________________________________________________ Part 5: Midsegment of a Triangle Theorem The Midsegment of a Triangle Theorem states that the misdsegment of a triangle is equal to __________ of the ______________ side _____________ setting up an equation, _______________ the midsegment by 2 and then solve. Example: Now you try: X X = ____________ Unit 8: Page 3 of 3 X = ____________