Download Honors Geometry Study Guide 1. Linear Pair 2. Vertical Angles 3

Honors Geometry Study Guide
1. Linear Pair
2. Vertical Angles
3.Altemate Interior Angles
4. Corresponding Angles
5. Base Angle Theorem
6. Midsegment of a Triangle: Midsegment Theorem
7. Coordinate Geometry
a. Midpoint Formula
( ~ +Xz
2
YI + YZ)
'
2
8. Polygons
a. Parallelograms: Properties: Sum of the angles = 360 Opposite sides are parallel Opposite sides and opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other
b. Rhombus: Additional Properties: Diagonals are perpendicular. Diagonals bisect a pair of opposite angles. Has 4 congruent sides. c. Square: Has 4 congruent sides and angles. Diagonals are congruent d. Rectangle: Diagonals are congruent
e. Kite: Diagonals are perpendicular
f. Trapezoid:
1. Isosceles Trapezoid
2. Midsegment Theorem
9. Ratio and Proportions
a. Solving
b. Simplifying
c. Problems involving area and perimeter.
10. Similar Polygons
a. Corresponding angles are congruent and corresponding sides are proportional .
b. Similarity Postulate and Theorems: AA, SSS, and SAS
c. Using proportionality theorems to calculate segment lengths
1. Triangle Proportionality Theorem (Th. 8.4)
2. Converse (Th 8.5)
3. If 3 parallel lines (Th. 8.6)
4. If a ray bisects an angle of a triangle, then it divides the opposite side into segments that
are proportional to the lengths of the other 2 sides. (Th. 8.7)
II.Geometric Mean: x=.j";:b
a. The altitude of a right triangle (Th. 9.2)
b. The length of a leg of a right triangle (Th. 9.3)
12. Pythagorean Theorem.
a. Classifying triangles.
1. Can the 3 sides form a triangle?
2. Right, acute, or obtuse
b. Special triangles
1. 45 - 45- 90: Hypotenuse = leg J2
2. 30 - 60 - 90: Longer leg = shorter leg .J3 and Hypotenuse = 2shorter leg
13. Trigonometry
a. soh - cah- toa
b. To fInd a side: use sin, cos, or tan (angle given) = fraction
c. To fInd a missing angle: use 2nd sin, cos, or tan (fraction) = A
14. Circles
a. Equation of a circle: ( x-hi + (y-ki = f2 with center (h,k) and radius r
b. Tangents
1. Perpendicular to the radius drawn to the point of tangency.
2. Two tangents from the same exterior point are congruent
c. Tangent and secant (lengths) : outsidee whole = outsidee outside d Secant and secant (lengths): outside e whole = outsidee whole e. Chord and chord (lengths): partl e part2 = partl e part2
f. Angles
1. central angle (vertex is the center) = measure of its arc
2. inscribed angles (vertex on the circle) = arc 2
3. tangent and chord (vertex on the circle)= arc
2
··de the CIrC
. I)
4. chord and chord (vertex IllS!
e arc + VA sarc
2
5. tangent&secant, tangent& tangent, or secant & secant
Big arc -Small arc
( vertex outside the circle)
2
I
g. Circumference : C = 2nf
h. Arc length
2
1. Area: A = r Jr
j. Area of a sector
15. Polygons
a. Interior angles: (n-2)e 180 = sum
b. Exterior angles: 360] = sum
c. Interior angle + exterior angle = 1800.
d. Area = ap
,..,
(Equilateral Triangle A = s2.J3
)
A
/
....J.
'-"