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Warm Up

Warm Up. Solve for r 1. 124= π r² 2. 136=(4÷3) π r³. Unit 1 Review. Solving For Vertical Angles. Set angles ____________to each other and solve. equal. 60. X + 2. Solving for Linear Pairs. Add together and set equal to ______________. 2x + 3. 55. 180. Adjacent Angles.

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Warm Up

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  1. Warm Up Solve for r 1. 124=πr² 2. 136=(4÷3)πr³

  2. Unit 1 Review

  3. Solving For Vertical Angles Set angles ____________to each other and solve equal 60 X + 2

  4. Solving for Linear Pairs Add together and set equal to ______________ 2x + 3 55 180

  5. Adjacent Angles Angles that are next to each other but DON’T create a ____________line 180

  6. Complementary angles =______ 90

  7. Supplementary angles =______ 180

  8. The Properties of Parallelograms A B • Opposite sides are congruent (AB=DC) • Opposite angles are congruent (D=B) • Consecutive angles are supplementary (A+D=180) • If one angle is right, then all angles are right. • The diagonals of a parallelogram bisect each other. • Each diagonal of a parallelogram separates it into two congruent triangles. C D

  9. opp. s  Example 1A WXYZ is a parallelogram. Find YZ. YZ = XW Def. of  segs. 8a – 4 = 6a + 10 Substitute the given values. Subtract 6a from both sides and add 4 to both sides. 2a = 14 a = 7 Divide both sides by 2. YZ = 8a – 4 = 8(7) – 4 = 52

  10. Alternate Interior Interior angles that lie on different parallel lines and opposite sides of transversal. They are equal to each other! n 1 2 m 4 3 5 6 t 8 7

  11. Alternate Exterior Angles formed outside the parallel lines and on opposite sides of transversal. They are equal! n 1 2 m 4 3 5 6 t 8 7

  12. Corresponding Angles that lie on the same side of the transversal and are situated the same way on two parallel lines. Think: Four CORNERS. They are equal! n 1 2 m 4 3 5 6 t 8 7

  13. Vertical Across the VERTEX from each other. They are equal! n 1 2 m 4 3 5 6 t 8 7

  14. Classifying Triangles Triangle – A figure formed when three noncollinear points are connected by segments. The sides are DE, EF, and DF. The vertices are D, E, and F. The angles are D,  E,  F. Angle E Side Vertex F D

  15. Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent. If , then

  16. Converse of Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent. If , then

  17. Right Triangles HYPOTENUSE LEG LEG

  18. Exterior Angles Interior Angles

  19. Triangle Sum Theorem The measures of the three interior angles in a triangle add up to be 180º. x + y + z = 180° x° y° z°

  20. Exterior Angle Theorem The measure of the exterior angle is equal to the sum of two nonadjacent interior angles 1 m1+m2 =m3 2 3

  21. The relationship shown in Example 1 is true for the three midsegments of every triangle.

  22. Example 1 Find each measure. BD ∆ Midsegment Thm. Substitute 17 for AE. BD = 8.5 Simplify.

  23. Solving for missing sides 4 6 x 18

  24. Find X X= 35 x 100˚ 45˚

  25. Solving for Linear Pairs Add together and set equal to ______________ 2x + 3 55 180

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