Transcript Algebra I - Denise Kapler
Unit 3
Congruent Triangles
Agenda
Rotate
Congruent Triangles
I know
that if two triangles are congruent, then one shape can become another through a Flip Slide
?
Within a plane are there other possible movements? Yes, the figure can be resized, but congruency is not preserved.
Word Movement in the plane
Octomber 2014
Agenda
Congruent Triangles
I know
that if two triangles are congruent, then the name of the triangles indicate the corresponding parts. βπ΄π΅πΆ β βπ·πΈπΉ
?
How are construction marks used to show how a triangle has been moved?
Word Corresponding parts
October 2014
Agenda
Congruent Triangles by SSS
I know
In Euclidean geometry any 3 points, when non-collinear, determine a unique
triangle
and a unique plane (i.e. a 2-dimensional Euclidean space).
?
How many ways can a triangle be proved congruent? (5) Word Non-collinear
October 2014
Agenda I know
Congruent Triangles By SAS
That congruent triangles are of the same size and shape. That they have the same side lengths and same angle measures .
?
Why do the angles of a triangle sum to 180Β°?
Word Classification of
ππ«π’ππ§π π₯ππ¬
October 2014
Agenda
Congruent Triangles by ASA
I know
That the exterior angle of a triangle equals the sum of the remote interior angles
?
What is a linear pair?
Word Remote Angles Exterior Angle
November 2014
Congruent Triangles
Agenda
By AAS
I know
That two triangles can share a side. Through the reflexive property these two shared sides can be shown to be congruent. π π β π π (see proof)
?
If you know the measures of two angles of a triangle, how do you calculate the third?
Word
Third Angle November 2014
Given: β NER β β πππ π π bisects β πΈπ π Prove: βπΈππ β βπππ
Agenda
Congruent Triangles by HL
I know
Given a right triangle that the hypotenuse is the longest side length. It is opposite the right angle. The right angle is formed by the legs.
?
Does it matter which leg is congruent when using HL?
Word Hypotenuse Leg
November 2014
Agenda
Congruent Triangles
I know
that if two triangles are congruent, then all corresponding parts are congruent. βπ΄π΅πΆ β βπ·πΈπΉ
NOTE: First prove
β β² π β
then use CPCTC to are prove corresponding parts are
β
?
How does the nomenclature of triangles help you determine correspondence?
Word CPCTC
October 2014
Agenda
Congruent Triangles
I know
Equilateral triangles are equiangular. All side lengths are congruent and all angle measures are congruent.
?
If you know the measures of two angles of a triangle, how do you calculate the third?
Word
Equi β Latin root word means same or equal November 2014
Agenda
Congruent Triangles
I know
If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse is true.
?
What is the definition of an isosceles triangle?
Word
Isos β Latin root word means equal. November 2014
Math Review October 29, 2014 1. Given the angles below, solve for β πΆ . (34Β° and 120Β°) 2. What is the relationship between β 3 and β 4? If β 3= 37 β°, solve for β 4. 3. Graph the following system. What is the relationship between the two lines? π¦ = π₯ + 1 2π₯ β 2π¦ = β2 1
A= bh A=s 1 +s 2 +s 3 A=lw; P=2l+2w A=Οr 2 C=2Οr y= mx + b defines linear
Math Review October 30, 2014 1. Given the 2 angles below, solve for x. (85Β° and 123Β°) 2. What is the relationship between β 5 and β 8? If β 5= 29 β°, solve for β 8. 3. Graph the following system. What is the relationship between the two lines? π¦ = π₯ + 1 8π₯ β 8π¦ = β8 1
A= bh A=s 1 +s 2 +s 3 A=lw; P=2l+2w A=Οr 2 C=2Οr y= mx + b defines linear
Math Review October 31, 2014 1. Given the angles below, solve for y. (42Β°, 85Β°, wΒ°, xΒ° and 88Β°) 2. What is the relationship between β 5 and β 8? If β 5= 29 β°, solve for β 8. 3. Graph the following system. What is the relationship between the two lines? π¦ = π₯ + 1 β2π₯ + 2π¦ = 2 1
A= bh A=s 1 +s 2 +s 3 A=lw; P=2l+2w A=Οr 2 C=2Οr y= mx + b defines linear
Math Review November 3, 2014 1. Given the angles below, solve for x,y,z. (xΒ°, yΒ°, zΒ°, 73Β° and 75Β°) 2. What is the relationship between β 2 and β 7? If β 2= 101 β°, solve for β 8. 3. Graph the following system. What is the relationship between the two lines? 4π¦ = 4π₯ + 4 β2π₯ + 2π¦ = 2
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think ) y= mx + b defines linear
Math Review November 4, 2014 1. Given the angles below, solve for x,y,z. (xΒ°, 144Β°, 72Β°) 2. What is the relationship between β 2 and β 7? If β 2= 101 β°, solve for β 8. 3. Graph the following system. What is the relationship between the two lines? 4π¦ = 4π₯ + 4 β2π₯ + 2π¦ = 2
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think ) y= mx + b defines linear
Math Review November 5, 2014 1. Given the angles below, solve for x. (61Β°, 73Β°, 72Β°)
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think )
2. What is the relationship between β 1 and β 5? If β 1= 37 β°, solve for β 8. 3. Graph the following system. What is the relationship between the two lines? 1 π¦ = π₯ 3 3π₯ + π¦ = 2
y= mx + b defines linear
Math Review November 6, 2014 1. Given the angles below, solve for β 1 πππ β 2 . (30Β°, 42Β°)
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think )
2. What is the relationship between β 1 and β 5? If β 1= 37 β°, solve for β 8. 3. Graph the following system. What is the relationship between the two lines? 1 π¦ = π₯ 3 3π₯ + π¦ = 2
y= mx + b defines linear
Math Review November 7, 2014 1. Given the angles below, solve for x. 2. What is the relationship 3. Graph the following [132Β°, 93Β°, (9x+3)Β°] between β 4 system. What and β 5? If is the β 5= 63 β°, relationship solve for β 3. between the two lines? 1 π¦ = π₯ 3 3π₯ + π¦ = 2
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think ) y= mx + b defines linear
Math Review November 10, 2014 1. Given the angles below, solve for 2. What is the relationship 3. Graph the following β π·π΄πΆ & β DCA between β 6 system. What [40Β°, 70Β°, 90Β°] and β 5? If is the β 5= 21 β°, relationship solve for β 2. between the two lines? 1 π¦ = π₯ 3 3π₯ + π¦ = 2
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think ) y= mx + b defines linear
Math Review November 11, 2014 1. Given the angles below, solve for 2. What is the relationship 3. Graph the following β π΄π΅πΆ & β ADC between system. What β 1and β 7? If is the β 1= 3 β°, solve relationship for β 7. between the two lines? 1 π¦ = π₯ 4 4π₯ + π¦ = 2
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think ) y= mx + b defines linear
Math Review November 11, 2014 1. Given the angles below, solve for β π 2. What is the relationship 3. Graph the following between β 4 system. What and β 8? If is the β 4= 63 β°, relationship solve for β 7. between the two lines? 1 π¦ = π₯ 3 3π₯ + π¦ = 2
Angle sum Triangle 180Β° Quadrilateral 360Β° Pentagon (think ) y= mx + b defines linear
Math Review September 11, 2014 1a. 400 If real: state if rational or irrational.
2. Find the distance between (-5, 24) and (2, 0) 3. Write the equation of the line defined by: (3, -2) and (-4, 5) 1b. Plot -10 < x <-1 on a number line Write the line equation in slope intercept form.
Real numbers exist on the number line
d
ο½ ο¨
y y
2 ο 1 ο© 2 ο« ο¨ 1 ο© 2
y= mx + b defines linear
Math Review September 15, 2014 1a. Determine area of square with side lengths of 2β 2. Find the midpoint between (-6, 24) and (2, 0) 3. Graph y= 1
x
1b. Determine perimeter of square with side lengths of 2β Name its function family
Area =
lw
Perimeter= 2
l
+ 2
w
y= mx + b defines linear
Math Review September 25, 2014 1a. Determine area of equilateral triangle s= 1cm 1b. Determine its perimeter 2. 2. Solve for x. Give algebraic reasons for each step.
6x + 7 = 22 - 3 3. Graph f(x) = -2 x Name its function family
Area =
lw
Perimeter= 2
l
ο°
r
ο°
+ 2
w
Given Properties of Real Numbers 1. Equality Under Operations: reflective, symmetric and transitive 2. Equality: Substitution 3. Simplify (Arithmetic)
y= mx + b defines linear