1. Final Exam
Key Concepts

2. Vertical Angles
Find the value of “x”.
68 = 2x + 32
36 = 2x
18 = x

3. Segments and Lengths
In the diagram, and S is the midpoint of QR = 4, and ST = 5. Find the following values.
RS =
PR =
PQ = 5 P Q R S T 10 6

4. Parallel Lines
Find the missing values.
70o
70o
110o

5. Straight Line is 180o
Find the difference between the larger angle and the smaller angle.
3x + (4x + 19) = 180
7x + 19 = 180
7x =161
x =23
3(23) = 69 and 4(23) + 19 = 111
111 – 69 = 42

6. Angles of Triangle = 180o 1x + 2x + 3x = 180 6x = 180 x = 30
The angles of a triangle are in the ratio of 1:2:3. Find the measure of each angle.
1x + 2x + 3x = 180
6x = 180
x = 30
30o, 60o, 90o

7. Exterior Angle Theorem
Find the missing value.
35o + 25o = 60o
60o

8. Angles and Sides of a Triangle
Remember, largest angle is OPPOSITE of longest side….
And smallest angle is OPPOSITE of smallest side.

9. TRIANGLE INEQUALITY THEOREM
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Is it possible for a triangle to have the following lengths?
3, 6, 8
6 + 3 = 9 > 8
YES

10. Three Theorems about Triangles
If c2 = a2 + b2, then the triangle is a right triangle.
If c2 < a2 + b2, then the triangle is an acute triangle.
If c2 > a2 + b2, then the triangle is an obtuse triangle. 12

11. RIGHT TRIANGLES

12. Special Right Triangles

13. Pythagorean Theorem
= x2
= x2
85 = x2

14. Pythagorean Triples
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25

15. Quadrilaterals

16. Quadrilaterals
Complete the worksheet.

17. 5 Ways to Prove Parallelograms
Both pairs of opposite sides are parallel
Both pairs of opposite sides are congruent
Both pairs of opposite angles are congruent
One pair of opposite sides congruent and parallel
Diagonals bisect each other.

18. SUM of the INTERIOR Measures of Any Polygon
(n – 2)180o
(8-2)180o = 1080o
(4-2)180o = 360o

19. Sum of the measures of the EXTERIOR angles of any polygon
h + o + r + s + e = 360o
c + r + a + p = 360o

20. A polygon that is both equilateral and equiangular.
REGULAR POLYGON
A polygon that is both equilateral and equiangular.

21. Areas

22. Circles

23. Angles in a Circle
80o
50o
50o
30o

24. Lengths in a Circle
12(9) = 18x
108 = 18x
6 = x

25. Lengths in a Circle
3(8) = 2(12)
24 = 24

26. Lengths in a Circle
122 = x(x+12+x)
144 = 2x2 + 12x
x = 8

29. SAT Formulas