UPCAT - MATH

Algebra, Geometry, Trigonometry, Basic Statistics, at Speed Math

Postulates

accepted as true without proof

Theorems

statement that can be proven

Postulate 1

A line contains at least two points

Postulate 2

A plane contains at least three non-collinear points

Postulate 3

Through any two points, there is exactly one line

Postulate 4

Through any three non-collinear points, there is exactly one plane

Postulate 5

If two points lie in the plane, then the line joining them lies in the plane

Postulate 6

If two planes intersect, then their intersection is a line

Theorem 1

If two lines intersect, then they intersect in exactly one point

Theorem 2

If a point lies outside a line, then exactly one plane contains both the line and the point

Theorem 3

If two lines intersect, then exactly one plane contains both lines

Phytagorean Theorem

c² = a² + b²

Hypotenuse

pinakamahaba

What is c?

10

What is x?

30

What is a?

52

What is x?

12

What is x?

13

What is y?

5√3

Point

zero-dimensional

Line

one-dimensional

Plane

two-dimensional

Space

three-dimensional

Ray

extends infinitely in one direction (have one endpoint)

Line Segment

is finite (have two endpoints)

When two lines intersect each other, what are formed?

Angles

The two lines will never intersect

Parallel Lines

Acute Angle

0°<, <90° (di pwedeng maging saktong 90°)

Right Angle

90°

Obtuse Angle

180°>, >90° (hindi aabot sa 180°)

Straight Angle

180°

Reflex Angle

>180°

If ∠a and ∠b are complementary angles and ∠a is 25°, what is the measurement of ∠b?

65°

If ∠a and ∠b are supplementary angles and ∠a is 25°, what is the measurement of ∠b?

155°

If ∠1 is 42°. Find the measurement of these angles:

∠a = 138°
∠b = 42°
∠c = 48°

Polygon

A shape with many sides

Regular Polygon

All sides are equal

Interior Angle

Angles are inside

Exterior Angle

Kadugtong ng Interior Angle para maging supplementary angle

How many sides is triangle

3

How many sides is quadrilateral

4

How many sides is Pentagon

5

How many sides is Hexagon

6

How many sides is Heptagon/Septagon

7

Sum° of triangle

180

Sum° of Quadrilateral

360

Sum° of Pentagon

540

Sum° of Hexagon

720

Sum° of Heptagon/Septagon

900

Regular Interior Angles Formula

(n - 2) x 180°/n

What is the sum of the interior angles of a polygon with 12 sides

1800°

Sum of Interior Angles Formula

(n - 2) x 180°

What is the measurement of an interior angle of a regular polygon with 12 sides?

150°