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
Noether's theorem wikipedia , lookup
History of geometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
Multilateration wikipedia , lookup
Linear programming wikipedia , lookup
Line (geometry) wikipedia , lookup
Name: Date: Page 1 of 2 Activity 2.5.2 The Vertical Angles Theorem The Linear Pair Postulate 1. In the figure at the right, C lies between β‘ . Name the linear points A and B on π΄π΅ pair of angles. 2. Find the sum of the measures of the linear pair. 3. With pencil and straightedge or software draw another linear pair of angles. 4. Measure the two angles you have drawn and find their sum. 5. A pair of angles is called supplementary if the sum of their measures is 180°. The Linear Pair Postulate states that if two angles form a linear pair, then they are __________________. Applying the Linear Pair Postulate 6. In the figure at the right mβ πΉππ» = 38°. Use the Linear Pair Postulate to find mβ π»ππ½ = _____ mβ π½ππΊ = _____ mβ πΊππΉ = _____ 7. Name two pairs of vertical angles in the figure above. What do you notice about their measures? 8. In the figure at the right mβ πΈππΏ = 103°. Use the Linear Pair Postulate to find mβ πΏππΌ = _____ mβ πΎππΈ = _____ mβ πΌππΎ = _____ 9. Name two pairs of vertical angles in the figure above. What do you notice about their measures? 10. Write a conjecture about vertical angles: Activity 2.5.2 Connecticut Core Geometry Curriculum Version 1.0 Name: Date: Page 2 of 2 On the previous page you may have conjectured that every pair of vertical angles are congruent. Now you can prove this conjecture as a theorem. Give a justification for each step. The Vertical Angles Theorem: If two lines intersect, then a pair of vertical angles formed are congruent. Given: Lines l and m intersect at Q. β 1 and β 2 are a pair of vertical angles. Prove: mβ 1 = mβ 2. Proof: 1. mβ 1 + mβ 3 = 180° Why? 2. mβ 2 + mβ 3 = 180° Why? 3. mβ 1 + mβ 3 = mβ 2 + mβ 3 Why? 4. mβ 1 = mβ 2 Why? Activity 2.5.2 Connecticut Core Geometry Curriculum Version 1.0