Health Careers Academy Mrs. Mitchell – Geometry 1-2 – Period: Gray- 1
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Transcript of Health Careers Academy Mrs. Mitchell – Geometry 1-2 – Period: Gray- 1
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Health Careers Academy Mrs. Mitchell – Geometry 1-2 – Period: Gray- 1
This report was done by Valentino J. Silva
Angles in Life Project
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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
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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°.
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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!
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Obtuse AngleAn obtuse angle is more than 90° but less than 180°
The image to the left is an angle between 90° and 180°.
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Straight AngleA straight angle is 180°
The image to the left gives an example of a straight angle.
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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.
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Supplementary Angles Two Angles are Supplementary if they add up to 180
degrees
120°
60°
60° + 120° = 180°
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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.
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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.
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Parallel LinesAlways the same distance apart, never touching.
The two lines are side by side, if they extend longer they will never touch.
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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
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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.
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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
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Line, Ray, & Segments
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LineA geometrical object that is straight, infinitely long and infinitely thin.
An example of a line.
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RayA portion of a line which starts at a point and goes off in a particular direction to infinity.
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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.
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Algebra Examples
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Supplementary AnglesGiven:
m<QPR = 2x+122, andm<RPS = 2x+22
Find m<RPS...
Q SP
R
2x+122 2x+22
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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° .
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Bisected AnglesGiven:
2 lines, make line AB and DC “Bisected”.
A BD C
A
B
D
C
Mid
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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
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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.
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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 = .
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MidpointTherefore, the midpoint between (1, 2) and (3, –2) is (2, 0).
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The End!!