III. Polygons
a) Sum of the interior angles: S = (n ā 2)180
b) Measure of an exterior angle: 360
ø
n
IV. Triangles
a) Sum of the angles = 180
b) Angles opposite equal sides are =
c) An exterior angle of a triangle equals the sum of the 2 interior angles that are āoppositeā the exterior angle.
70
x = 70 + 65
x =135
x 65
d) The sum of any two sides of a triangle must be greater than the third side.
Ex) A triangle could not have sides with length 1, 4 and 5 because 1 + 4 = 5 (has to be greater)
V. Know properties about quadrilaterals: parallelograms, rectangles, squares, rhombus, and trapezoids.
VI. Know āmethodsā to prove triangles congruent:
SSS, SAS, AAS, ASA,HL
VII. Sides of similar figures form proportions. (Be sure to match up sides)
16 16 x 12 8
8
12
VIII. Know perimeter and area formulas.
Perimeter: add up the sides.
Circle ā Circumference: C =
p
d
Area:
A = bh (parallelogram)
A = Ā½ bh (triangle)
A = Ā½ h(b1 + b2) (trapezoid)
A =
p
r2 (circle)
IX. Know what happens if I were to change the side of a figure what would happen to the area. For example, if I double the radius of a circle what happens to the area?
X. Proportions in right triangles
a) left segment altitude b) hypotenuse leg altitude right segment leg adjacent segment
XI. Pythagorean Theorem: c2 = a2 + b2
XII. Special Right Triangles: 45-45-90 and 30-60-90
XIII. Trig: Sine, Cosine, and Tangent
XIV. Distance and Midpoint
D =
Ö
(x2 ā x1)2 + (y2 ā y1)2
M = x1 + x2y1 + y2 2 2
XV. Coordinate Geometry Proofs
TEST 4 REVIEW PROBLEMS
TEST 4 REVIEW PROBLEMS
1. Find the sum of the interior angles of a pentagon.
2. If the circumference of a circle is 12
p
, find the area of the circle.
3. A 5x ā 60 B
C
x +20
D E
Find the measure of angle ACD.
3. The measure of angle CBD is 165. The measure of angle BAC is 80. Find the measure of angle ACB.
C
A B D
4. Find the distance and midpoint of the following points (-2, 3) and (4, -1)
5. Triangle ABC ~ Triangle DEF. Find x.
12 12
15
10 x
6.Find the area of the shaded figure.
20
13
15
12
7. If the diameter of a circle is doubled, then the circumference would
A. Multiply by 4 B. is halved C. Doubled D. Increases by 2
8. Give an example of a Pythagorean Triple. Show why itās a Pythagorean Triple.
9. If two sides of a triangle measure 4 and 7, the length of the third side could be
A. 11 B. 2 C. 3 D. 10