health careers academy mrs. mitchell – geometry 1-2 – period: gray- 1

Health Careers Academy Mrs. Mitchell – Geometry 1-2 – Period: Gray- 1

This report was done by Valentino J. Silva

Angles in Life Project

Table of Contents

Angles●Acute Angle●Right Angle●Obtuse Angle●Straight Angle●Complementary/Supplementary Angle●Bisected Angle●Vertical Angle●Congruent Angle

Lines●Parallel Line

Points●Collinear Points

Line, Ray, & Segment●Line●Ray●Segment

Algebra Examples

Acute AngleAn acute angle is a angle less than 90°

In the image to the left, is at an acute angle. The angle is less than 90°.

Right AngleA right angle is an internal angle which is equal to 90°

The image below, is a right angle. Which is exactly 90°.

Only 90° equals a right angle!

Obtuse AngleAn obtuse angle is more than 90° but less than 180°

The image to the left is an angle between 90° and 180°.

Straight AngleA straight angle is 180°

The image to the left gives an example of a straight angle.

Complementary AnglesTwo Angles are Complementary if they

add up to 90 degrees (a Right Angle)

Measure 1

Measure 2

M<1, can be 89° and M<2, can be 1°. That will equal 90° once you add them.

Supplementary Angles Two Angles are Supplementary if they add up to 180

degrees

120°

60°

60° + 120° = 180°

Bisected Angle"Bisect" means to divide into two equal parts.

You can bisect lines, angles, and more.

The image to the left has bones that are bisected.

Vertical AngleAre the angles are opposite of each other when two

lines crossThe image to the left has a “X” in it.

The “X” can be represented as a vertical angle.

Parallel LinesAlways the same distance apart, never touching.

The two lines are side by side, if they extend longer they will never touch.

Congruent LinesCongruent line segments are lines that have the same length

Her arms are an example of congruent lines. Both arms are the same length.

=

Both have the same length

Collinear PointsA set of points that lie in a straight line

The joints in the legs can act like collinear points.

Points P,Q,R,S are collinear, in the image below.

Midpoint

The midpoint on the wall is divided into two half’s, two equal half’s

Point on a line segment dividing it into two segments of equal length

Line, Ray, & Segments

LineA geometrical object that is straight, infinitely long and infinitely thin.

An example of a line.

RayA portion of a line which starts at a point and goes off in a particular direction to infinity.

SegmentThe set of points consisting of two distinct points and all in between them.

The image to the left, is an example if a segment of a finger.

Algebra Examples

Supplementary AnglesGiven:

m<QPR = 2x+122, andm<RPS = 2x+22

Find m<RPS...

Q SP

R

2x+122 2x+22

Supplementary AnglesStep #1: Add them up. Step #2RPS: Plug them into m<RPS

2x + 122 + 2x + 22 = 180° 2x + 22 = ??

4x + 144 = 180° 2(9) + 22 = -144 -144 ----------------------- 18 + 22 = 404x = 36 ---- ----4x 4x m<RPS = 40°

x = 9

It equals 180° because its one the straight line which is 180° .

Bisected AnglesGiven:

2 lines, make line AB and DC “Bisected”.

A BD C

A

B

D

C

Mid

Proof Referring to Figure 1, we are going to prove that a=b and y=s Note thata + y = 180° (because angles a and y make in sum the straight angle), and b + y = 180° (because angles y and b make in sum the straight angle). …....a=b.

Similarly,a + s = 180° (because a and s make in sum the straight angle) anda + y = 180° (because a and y make in sum the straight angle). Therefore, y=s. The proof is completed.

ExampleIf in figure1 one of vertical angles a = 37°, find three other angles b, y and s.

Solutionb = 37° as the vertical angle to a;Y = 180°- 37° = 143° as the complementary angle to a;s = 143° as the vertical angle to y.

Vertical Angles

Figure 1

MidpointFind the value of p so that (–2, 2.5) is the midpoint between (p, 2) and (–1, 3).

I'll apply the Midpoint Formula:

Find the midpoint between the points (1, 2) and (3, -2) shown on the grid below.

Midpoint.

To do this, we first look at a number line and find the midpoint between x = 1 and x = 3.

The principle that we apply will give us a general formula for the midpoint between any two points with given coordinates. The point that is exactly halfway between 1 and 3 on this one-dimensional number line is 2. This can be found by averaging the 2 coordinates:

If we apply the averaging strategy to our two points, we have: x = .

MidpointTherefore, the midpoint between (1, 2) and (3, –2) is (2, 0).

The End!!