ACT Math: Geometry I - Amazon S3

ACT Math: Geometry I

1 / 29

Geometry I

Learning Objectives

By the end of this lesson, you will be able to: ? Use given values to determine the measure of unknown

angles ? Use the properties of parallel and perpendicular lines to

determine slope ? Recognize types of triangles and their respective properties ? Use the Pythagorean theorem and special right triangles to

determine unknown values ? Solve problems using common trigonometric concepts ? Define key terms and relationships of circles

2 / 29

Angles

Types of Angles

Right angles measure exactly 90? Acute angles measure less than 90? Obtuse angles measure more than 90?

Right Angle

Acute Angle

Obtuse Angle

3 / 29

Angles

Types of Angles

Complementary angles add up to 90?

Supplementary angles add up to 180?

Vertical angles are opposite each other when two lines cross. Vertical angles

are congruent

a = d

b = c

x? y?

Complementary Angles

Supplementary Angles

Vertical Angles 4 / 29

Angles

1. In the figure below, points A, B, and C are on a straight line. What is the measure of angle DBE?

A. 60? B. 80? C. 100? D. 120? E. 140?

E

D

20?

40?

A

B

C

5 / 29

Angles

Parallel and Perpendicular Lines Parallel lines always have the same slope

They never intersect!

Perpendicular lines have negative reciprocal slopes

These lines intersect at a 90? angle

y

x

Parallel Lines

y slope = 2

x slope = ??

Perpendicular Lines

6 / 29

Angles

Parallel Lines and Transversals

When two parallel lines are cut by a transversal:

All of the acute angles are equal:

b = d = f = h

All of the obtuse angles are equal:

a = c = e = g

Any acute and obtuse angle are supplementary:

a + h = 180 b + e = 180, etc

7 / 29

Angles

2. In the figure below, AC is parallel to DF. PQ intersects AC at point B and intersects DF at point E. Which of the following must be true?

F. PBA + DEQ = 180? G. PBA + BED = 90? H. PBA = DEQ J. PBA = 90? K. DEQ = 90?

P

A

B

C

D

E

F

Q

8 / 29

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download