Final Exam Key Concepts.

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6.2 Properties of Parallelograms

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Presentation transcript:

Final Exam Key Concepts

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

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

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

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

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

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

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

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

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

RIGHT TRIANGLES

Special Right Triangles

Pythagorean Theorem 62 + 72 = x2 36 + 49 = x2 85 = x2

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

Quadrilaterals

Quadrilaterals Complete the worksheet.

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.

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

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

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

Areas

Circles

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

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

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

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

SAT Formulas