The (Ultimate) Geometry Review Sheet Page 10
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Triangle Angle Bisector Theorem (side proportions) - If a ray bisects an angle of a triangle,
then it divides the opposite side into segments proportional to the other two sides.
Right Triangle Altitude Theorem - If the altitude is drawn to the hypotenuse of a right triangle,
then the two triangles formed are similar to the original triangle and each other.
Corollary 1 of Right Triangle Altitude Theorem - When the altitude is drawn to the
hypotenuse of a right triangle, the length of the altitude is the geometric mean between the
segments of the hypotenuse.
Corollary 2 of Right Triangle Altitude Theorem - When the altitude is drawn to the
hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and
the segment of the hypotenuse that is adjacent to the leg.
If two triangles are similar, then the ratio of any two corresponding segments (such as medians,
altitudes, angle bisectors) equals the ratio of any two corresponding sides.
Pythagorean Theorem - In a right triangle, the square of the hypotenuse is equal to the sum
of the squares of the legs.
Converse of Pythagorean Theorem - If the squares of one side of a triangle is equal to the
sum of the squares of the other two sides, then the triangle is a right triangle.
Some Resources:
(A listing of materials.)
(More specific listings.)
(More general problems.)
Videos:
(The basics.)
(Examples.)
(More of the general ideas.)
CIRCLES
You should be very comfortable with finding the area of a circle, and working with diameter, radius, and
circumference.
A brief outline of the rules for different (secants, tangents, segments) in a circle:
Get some practice with:
Chords and circles:
Tangents and circles:
Mixed practice (secants, tangents, and chords):
Know the key theorems for angles both inside and outside of a circle. You should have a graphic organizer with
these formulas, but you can also check here for an overview of all the angles of a circle:
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education