Post on 19-Jan-2016
M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope
GSE:
M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or across disciplines or contexts (e.g., Pythagorean Theorem
G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
AA BB
Point A is at 1.5 and B is at 5.
So, AB = 5 - 1 1.5 = 3.55 = 3.5
Find the measure of PR
Ans: |3-(-4)|=|3+4|=7
Would it matter if I asked for the distance from R to P ?
1) Pythagorean Theorem- Can be used on and off the coordinate plane
•2) Distance Formula – only used on the coordinate plane
* Only can be used with Right TrianglesWhat are the parts to a RIGHT Triangle?1. Right angle2. 2 legs3. Hypotenuse
Right angle
LEG
Leg – Sides attached to the Right angle
Hypotenuse- Side across from the right angle. Always the longest side of a right triangle.
222 )()()( hypotenuselegleg
Make a right Triangle out of the segment
(either way)
Find the length of each leg of the right Triangle.
Then use the Pythagorean Theorem to find the Original segment JT (the hypotenuse).
Find the length of CD using the Pythagorean Theorem
10
88.12164
164
10064
108
2
2
222
DC
DC
DC
DC
We got 8 by | -4 – 4|
We got 10 by | 6 - - 4|
Find the missing segment- Identify the parts of the triangle
5 in
13 inAns: 5 2 + X 2 = 13 2
Leg 2 + Leg 2 = Hyp 2
hyp
Leg
Leg
25 + X 2 = 169
X 2 = 144
X = 12 in
Lets Use the Pythagorean Theorem
2122
12 yyxx
Identify one as the 1st point and one as the 2nd. Use the corresponding x and y values
(4-(-3))2 + (2-(5))2
(4+3)2 + (2-5)2
(7)2 +(-3)2
49+9 =58 ~ 7.6~
J (-3,5) T (4,2)
d =
x1, y1 x2, y2
Find the length of the green segment
Ans: 109 or approximately 10.44
Segments that have the same length.
If AB & XY have the same length,Then AB=XY,
butAB XY
Symbol for congruentfor congruent