1. Aim: Week 1 and 2 Concept Review (QUIZ AT 10:30!) Do Now: Copy the image and Complete the following "statement - reason" proofs. Given: AD|| EH. a. Prove that <ABE ≅ <BEF b. Prove that <EBF ≅ <GCH c. Prove that triangle CGH is a right triangle. (Requires at least 2 steps)

2. Using the Segment Addition Postulate If EG = 100, find the value of x. Then find EF and FG. EFG 4x - 202x + 30

3. Find the missing complementary angle. 64° ?°?°

4. The following angles are complementary. Solve for x. 2x + 5 x + 25

5. The following angles are supplementary. Solve for x. 2x + 10 3x + 20

6. In the figure a || b. 1. Name the angles congruent to  3. 2. Name all the angles supplementary to  6. 3. If m  1 = 105° what is m  3? 4. If m  5 = 120° what is m  2? 5. Name a pair of a. Alternate exterior angles b.Alternate interior c.Corresponding d.Vertical

7. Find the missing angles. 45 ° b° 50 ° d °75 ° Hint: The 3 angles in a triangle sum to 180°.

8. Another practice problem Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 40 ° 120°

9. Related Regents Question A transversal intersects two lines. Which condition would always make the two lines parallel? 1)Vertical angles are congruent. 2)Alternate interior angles are congruent. 3)Corresponding angles are supplementary. 4)Same-side interior angles are complementary.

10. Related Regents Question In the diagram above, line p intersects line m and line n. If <1 = 7x and <2 = 5x+30, lines m and n are parallel when x equals 1)12.52)15 3)87.54)105

11. Ex. : Interior Angles of a Quadrilateral 80° 70° 2x° x°x° Find the measure of each angle in the quadrilateral?

12. Example: Find m<1 Find m<2 Find m<3 28 82 68 2 1 3

13. Example The diagram is a map showing John's house, Kay's house, and the grocery store. What is the angle the two houses make with the store? y = 12, Store = 30°

14. Think-Pair-Share Can a right triangle contain an obtuse angle? Explain.

15. Related Regents Questions The degree measures of the angles of Triangle ABC are represented by x, 3x, and. Find the value of x.

16. Related Regents Questions DEF is a right triangle, <D = 90 and <F is 12 degrees less than twice <E. Find E and F.

17. Example: Applying the Third Angles Theorem Find mP and mT.

18. 18 Ex. 3 Finding an Angle Measure. 65  xx Exterior Angle theorem: m  1 = m  A +m  1 (2x+10) 

19. Find mACD. Example

20. Regents Question

21. Related Regents Questions What is the measure of <LKN?

22. Mid-Segments Given: Segment FE is the mid-segment of triangle ABC. Point D is the midpoint of BC. m ∠ FAE = 75° and m ∠ FEC = 120° AF = 5.6 ft., EC = 4.5 ft., and BC = 12.5 ft Fill in all missing information.

23. Related Regents Questions In the diagram above, D is the midpoint of AC, O is the midpoint of AT, and G is the midpoint of CT. If AC = 10, AT = 18, and CT = 22, what is the perimeter of parallelogram CDOG?

24. Related Regents Questions Find the perimeter of the triangle formed by connecting the midpoints of the sides of Triangle ABC

25. Khan Academy Week 1 & 2 Recognizing rays lines and line segments Parallel lines 1 Points lines and planes Combining like terms Combining like terms with distribution Alternate exterior angles Same side exterior angles Alternate exterior angles 2 Same side exterior angles 2 Segment Addition Midpoint of a Segment