bellringer 67° x°x° y°y° x = ? y = ? this is a base angle of an isosceles triangle. it must...

BELLRINGER 67° x° y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x = 113° Lastly, use TAS to find y. 67 + 90 + y = 180 y = 23°

Upload: elijah-woods

Post on 13-Jan-2016

219 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

BELLRINGER

67°

x°

y°x = ?

y = ?

This is a base angle of an isosceles triangle. It must measure 67°

Find x by using LP. 67 + x = 180.

-67 -67

x = 113°

Lastly, use TAS to find y. 67 + 90 + y = 180

y = 23°

Page 2: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

What is the maximum number of congruent angles in a Scalene Triangle? In an equilateral triangle, we already

showed that all 3 angles are congruent. (60, 60, 60).

In an isosceles triangle we showed that TWO angles are congruent, the base angles.

Thus, there can be NO angles congruent in a scalene triangle, otherwise it would be isosceles or equilateral.

Page 3: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

Triangle Angle-Side Relationships

You will find that the largest angle in a triangle corresponds to the longest side, and the smallest angle corresponds to the shortest side.

For example, name the sides from shortest to longest!

r68

q, p, r z, x, y

Page 4: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

In Other Words,

LARGEST

LONGEST

SMALLEST

SHORTEST

Page 5: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

What is a median?

The median of a triangle connects a vertex to the opposite side’s midpoint.

Z The three medians of any triangle are concurrent at the CENTROID.

Page 6: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

Special segments of a triangle Can you find the altitude, angle

bisector, median, perpendicular bisector, and midsegment??

Altitude

Angle Bisector

Median

Perpendicular Bisector

Midsegment

Page 7: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

Summarize our findings . . .

The angle bisectors of a triangle are concurrent at the incenter. The circle centered at the incenter is inscribed in the triangle.

The perpendicular bisectors of a triangle are concurrent at the circumcenter. The circle centered at the circumcenter circumscribes the triangle.

The altitudes of a triangle are concurrent at the orthocenter. (We will investigate the orthocenter after break).

The medians of a triangle are concurrent at the centroid. The centroid is the center of mass of the triangle.

Page 8: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

Picture it all together . . .

A = altitudes

B = angle bisectors

C = medians

D = perpendicular bisectors

Page 9: BELLRINGER 67° x°x° y°y° x = ? y = ? This is a base angle of an isosceles triangle. It must measure 67° 67 Find x by using LP. 67 + x = 180. -67 -67 x

Hiding the lines . . .

A = altitudesB = angle bisectorsC = mediansD = perpendicular bisectors

Reflection 2 Reflecteach shape in the mirror line. a) 1 a ...blog.lostock.bolton.sch.uk/.../Lesson-3-Reflection.pdf · © White Rose Maths 2020 x y x y x y x y x y x y x y x y x y

Plot (x-values, y-values) >> x = linspace (-3, 3, 20); >> x = linspace (-3, 3, 20); >> y = 2*x – 1; >> y = 2*x – 1; >> plot (x, y) >> plot (x, y)

Examples and Sets. Synthesize each of These choose((x,y) =>10 x + 14 y == a) choose((x,y) =>10 x + 14 y == a&& x < y) choose((x,y) =>10 x + 14 y == a

Heath y Carter 67

Order of operators: 1.x ** y Power (right associative) 2.x * y, x / y, x // y, x % y Multiplication, division, floor division, modulo 3.x + y, x - y Addition,

Wave Physicsphyweb.phys.soton.ac.uk/quantum/lectures/waves/waves17...Plucked guitar string L x y x,t x x L-x L+x y x y x y L x y L x •boundary conditions: Acoustic waves ... •register

Algebra Days 1-10 · a2 a x a y³ ÷ y 4 = y³ = y x y x y = 1 = y −1 y4 y x y x y x y y 1 (y³)² = (y x y x y )² = y x y x y x y x y x y = y 6 y0 = 1 Recognising and collecting

Numéro Annexe A · 2005. 9. 13. · 67-66-3 Chloroforme Chloroform Cloroformo X X X 67-72-1 Hexachloroéthane Hexachloroethane Hexacloroetano X X X 68-12-2 N,N-Diméthyl formamide

Reflection 2 Reflecteach shape in the mirror line. a) 1 a) d) e)s3-eu-west-1.amazonaws.com/smartfile/8f31e6980b1ab7f62a...© White Rose Maths 2020 x y x y x y x y x y x y x y x y x

X= {x 0, x 1,….,x J-1 } Y= {y 0, y 1, ….,y K-1 } Channel Finite set of input (X= {x 0, x 1,….,x J-1 }), and output (Y= {y 0, y 1,….,y K-1 }) alphabet

> plot(cos(x) + sin(x), x=0..Pi); plot(tan(x), x=-Pi..Pi ... · > plot3d({sin(x*y), x + 2*y},x=-Pi..Pi,y=-Pi..Pi); ↵ c1:= [cos(x)-2*cos(0.4*y),sin(x)-2*sin(0.4*y),y]: ↵ c2:= [cos(x)+2*cos(0.4*y),sin(x)+2*sin(0.4*y),y]:

X y (x,y) x - coordinate y - coordinate. How are coordinates helpful?

2D Transformations. Translation x’ = x + tx y’ = y + ty translation vector: T = P = P’ = P’ = P + T x y (x,y) (x’,y’) tx ty xyxy x’ y’

Input 1 Output - Texas A&M University multipliers... · 2020. 10. 30. · ds (Type I) I1 I2 I3 I4 Y y X x Y y X x X x I01 I02 Zf V0 Y y X x Y y X x X x I01 I02 MS Vb Rf1 Rf 2 Vdd

Increment Operator To increment a variable X by 1. X+1;X+=;++X; X = 10 Y = X + 1;Y = 11 X += 1;X = 11 Y = ++X + 4;Y = 15

K x x y x - WordPress.com · 2018. 6. 10. · 6 Q | x | y a x { x y | | y | | : ^ x x x | x { x x x x x | | x x y | x , x { x x x ~

Special Products a(x + y + z) = ax + ay + az (x + y)(x – y) = x 2 – y 2 (x + y) 2 = x 2 + 2xy +y 2 (x – y) 2 = x 2 – 2xy +y 2 (x + y + z) 2 = x 2 + y

X x ,x x,y y x - pvmouche.deds.nl

57 ¼” x 67 ½” Rain or Shine - Moda Fabrics

Acrylated Silicones Suitable for SLA 3D [email protected], 416-424-4567 x y Reactive Silicones x y x y x y x y x y x y Hydroxy Acrylate Acrylate Acrylated Silicone Types

Evergreen 5 67 x 7.ai

imag · #typedef unsigned if_sqn_set_type; #define if_sqn_set_copy(x,y) (x)=(y) #define if_sqn_set_compare(x,y) (x)-(y) #define if_sqn_set_print(x,f) fprintf(f,"%#x",x) #

4 4 9€¦(y - y ) ( ) 7 3( 2) 7 3 6 Point-Slope form 7 3 67 m x x m x x yx yx yx 3 1

Basic Sets - Mathematics | Michigan State University · MTH299 - Examples Scratch Work: x x 1 = y x= y(x 1) x= yx y x xy= y x(1 y) = y x= y 1 y and let x= y 1 y then we can see that:

Town of MinocquaTRL Voting Wards · 2018. 1. 3. · xy xy xy xy xy xy xy xy xy xy xy xy xy xy xy xy xy xy x y x y x y x y x y x y x x x x y x y x y x y x y x y x y x y x y x y x y

DSP Slide 1 Graph theory x y y = x x y a y = a x x z y y = x and z = x xz y z = x + y z = x - y xz y - y = z -1 x x y z -1 DSP graphs are made up of points

Quilt is 67½x Quilt is 67½x75. - Moda Fabrics. Moda HomeQuilt is 67½"x Quilt is 67½"x75". Created Date: 9/29/2011 3:14:54 PM

X Y means X calls Y

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS€¦ · (a3): (8 x;y;z 2 X ) (( x y ) z = ( x z) y ), (a4): (8 x;y;z 2 X ) (( x z) (y z) x y ), where x y if and only if x y = 0

Summer Work Packet For Students Entering Algebra 1 Honors€¦ · x x y 8) x x y y x x y 10) y x x 11) y x x y 12) y x x y ©Y i2j0 Z1j2 3-2-xKauIt ya 1 uSqozf xtSw 3a or 1ee wLhLqCL.0

ö - Echo360€¦ · - /$)"x )x #*÷ûôx1$ *x ..$")( )/x$)x/# x ** ' x x + " xõx*!xö yyyyy y # y1$ *y ..$")( )/y! /0- y ''*2.y./0 )/.y/*y - / y $/y( ) " y ) y.0 ($/y1$ *y *)/ )/y!*-

+X +Y +X +Y +X +Y slope of tangent = dy/dx. y a x y a x y a x

62 - 67 X Body GM - Jegs High Performance...62 - 67 X Body GM Installation Instructions Manual Disc Conversion 62 - 67 X Body DBMC09 & PVK71 pictured above (Booster, master & valve

Linear and affine functions - Slope-intercept form...-3-65) x y 66) x y 67) x y 68) y 69) x y 70) x y 71) x y 72) x y 73) x y 74) y 75) x y 76) x y 77) x y 78) x y 79) x y 80 ) x y

1 Elementary Functions - Elsevier.com · 2013. 12. 20. · 3. cos2 x−sin2 y =cos(x+y)cos(x−y) = cos2 y −sin2 x 4. sinh2 x+cosh2 y =cosh(x+y)cosh(x−y)=cosh2 x+sinh2 y 1.316