1. Geometry Final Exam Review Materials Prepared by Francis Kisner June 2015

2. Proportional Reasoning If 12 eggs are enough for one recipe that will feed 8 people, how many eggs will be needed to serve 20? Congruent line segments are the same length. Congruent angles are the same measure. Comparing two polygons that look the same shape, if all the sides of one are the same multiple of the sides of the other, the sides are said to be proportional. What do you have if the angles of the two polygons are congruent and the corresponding sides are proportional? What does the symbol “~” mean in geometry?

3. If you have two similar polygons and you know the perimeter of one and you know the “scale factor”, can you find the perimeter of the other? Example: You have two trapezoids that are similar. One is ¾ the size of the other. The larger has sides measuring 6, 2, 4, 4 inches. Can you tell the perimeter of the smaller trapezoid?

4. Conditions giving similar triangles. AA, SAS, SSS Pages 381-395 In triangles, knowing that the angles of two triangles are the same is enough to show that the triangles are similar. If corresponding sides are equal then the triangles are congruent. When two lines cross they create two sets of angles. Within each set, the angles have the same measure. ( Vertical Angles ) If a line (a transversal) is drawn across two parallel lines, the corresponding angles formed are equal. (Literally, all the acute angles are the same and all the obtuse angles are the same.)

5. The Triangle Proportionality Theorem and Converse See pages 397 and 398 If a line parallel to one side of a triangle intersects the other two sides, it divides the two sides proportionally. If a line divides two sides of a triangle proportionately, then it is parallel to the third side. --- If three parallel lines intersect two transversals, they divide the transversals proportionately. If a ray bisects an angle of a triangle, it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. See page 398

7. Know the definitions of the Trig Functions In a right triangle, when you are looking at an angle between a leg and the hypotenuse: Sin = opposite leg / hypotenuseCos = adjacent leg / hypotenuse Tan = opposite leg / adjacent leg Know how to find the functions on your calculator. Given the value of a function, know how to find the angle.

9. Know how to find the sum of the interior angles of a polygon. How does the sum relate to the number of sides? Know the sum of the exterior angles of a polygon. Does the sum relate to the number of sides?

10. Special Quadrilaterals Know the definitions and characteristics of SquareRectangleParallelogram RhombusTrapezoidKite Which have parallel sides? How many parallel sides do they have? Is there any special characteristic of the diagonals?

11. What do you know about parallelograms? Sides?Opposite AnglesConsecutive angles Opposite SidesDiagonals? What do you know about trapezoids? Sides?AnglesOpposite Sides? If we know the lengths of the bases, can we find the length of a line connecting the centers of the other two sides? What do you know about isosceles trapezoids? Base angles? Opposite sides?Diagonals? Base segments? Sides?

12. What do you know about kites? Diagonals?Opposite Sides?Consecutive Side Pairs? Opposite Angles?Interior Angles? What do you know about rectangles? Sides?Angles?Diagonals?

13. Circles, Tangents, Chords, Etc. If the tangent is 20cm long and the line from the center A to the top vertex is 25 cm long, how long is the radius of the circle? 25 20 A If mPR = 90º and PQ = QR, find mQR P R Q

14. What do you know about triangles inscribed in circles? What do you know if one side of the inscribed triangle is a diameter of the circle? Tangents and Chords P If the angle between the chord PQ and the tangent line is 80º, What is the measure of arc PQ ? Q

15. 150º P Q 100º S R If the angle between the chords is 100º and the arc PA measures 150º, what is the size of arc RS?

16. Do you know about the proportions of intersecting chords? If you know the lengths of some of the segments, can you find the others? If you know some of the lengths of segments of Secant Lines, can you find the others?

17. If you know the measure of arc ADC is 170º, can you find the measure of A angle ADC? B D C What do you know about the relationship between the radius of a circle and a chord of the circle? Do you know any other facts about the chord and the radius?

18. Can you find the area of a rectangle? Can you find the height of a triangle if you know the base and the area? Can you find the area of a parallelogram if you have the base and the height? Can you find the area of a kite if you have the lengths of the two diagonals?