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. ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹

?

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 180°?

Word Classification of

𝐓𝐫𝐢𝐚𝐧𝐠𝐥𝐞𝐬

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. 𝑅𝑁 ≅ 𝑅𝑁 (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: ∠ NER ≅ ∠𝑁𝑉𝑅 𝑅𝑁 bisects ∠𝐸𝑅𝑉 Prove: ∆𝐸𝑁𝑅 ≅ ∆𝑉𝑁𝑅

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. ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹

NOTE: First prove

∆ ′ 𝒔 ≅

then use CPCTC to are prove corresponding parts are

≅

?

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 – 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 – Latin root word means equal. November 2014

Math Review October 29, 2014 1. Given the angles below, solve for ∠𝐶 . (34° and 120°) 2. What is the relationship between ∠3 and ∠4? If ∠3= 37 ⁰, solve for ∠4. 3. Graph the following system. What is the relationship between the two lines? 𝑦 = 𝑥 + 1 2𝑥 − 2𝑦 = −2 1

A= bh A=s 1 +s 2 +s 3 A=lw; P=2l+2w A=πr 2 C=2πr y= mx + b defines linear

Math Review October 30, 2014 1. Given the 2 angles below, solve for x. (85° and 123°) 2. What is the relationship between ∠5 and ∠8? If ∠5= 29 ⁰, solve for ∠8. 3. Graph the following system. What is the relationship between the two lines? 𝑦 = 𝑥 + 1 8𝑥 − 8𝑦 = −8 1

A= bh A=s 1 +s 2 +s 3 A=lw; P=2l+2w A=πr 2 C=2πr y= mx + b defines linear

Math Review October 31, 2014 1. Given the angles below, solve for y. (42°, 85°, w°, x° and 88°) 2. What is the relationship between ∠5 and ∠8? If ∠5= 29 ⁰, solve for ∠8. 3. Graph the following system. What is the relationship between the two lines? 𝑦 = 𝑥 + 1 −2𝑥 + 2𝑦 = 2 1

A= bh A=s 1 +s 2 +s 3 A=lw; P=2l+2w A=πr 2 C=2πr y= mx + b defines linear

Math Review November 3, 2014 1. Given the angles below, solve for x,y,z. (x°, y°, z°, 73° and 75°) 2. What is the relationship between ∠2 and ∠7? If ∠2= 101 ⁰, solve for ∠8. 3. Graph the following system. What is the relationship between the two lines? 4𝑦 = 4𝑥 + 4 −2𝑥 + 2𝑦 = 2

Angle sum Triangle 180° Quadrilateral 360° Pentagon (think ) y= mx + b defines linear

Math Review November 4, 2014 1. Given the angles below, solve for x,y,z. (x°, 144°, 72°) 2. What is the relationship between ∠2 and ∠7? If ∠2= 101 ⁰, solve for ∠8. 3. Graph the following system. What is the relationship between the two lines? 4𝑦 = 4𝑥 + 4 −2𝑥 + 2𝑦 = 2

Angle sum Triangle 180° Quadrilateral 360° Pentagon (think ) y= mx + b defines linear

Math Review November 5, 2014 1. Given the angles below, solve for x. (61°, 73°, 72°)

Angle sum Triangle 180° Quadrilateral 360° Pentagon (think )

2. What is the relationship between ∠1 and ∠5? If ∠1= 37 ⁰, solve for ∠8. 3. Graph the following system. What is the relationship between the two lines? 1 𝑦 = 𝑥 3 3𝑥 + 𝑦 = 2

y= mx + b defines linear

Math Review November 6, 2014 1. Given the angles below, solve for ∠1 𝑎𝑛𝑑 ∠2 . (30°, 42°)

Angle sum Triangle 180° Quadrilateral 360° Pentagon (think )

2. What is the relationship between ∠1 and ∠5? If ∠1= 37 ⁰, solve for ∠8. 3. Graph the following system. What is the relationship between the two lines? 1 𝑦 = 𝑥 3 3𝑥 + 𝑦 = 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 [132°, 93°, (9x+3)°] between ∠4 system. What and ∠5? If is the ∠5= 63 ⁰, relationship solve for ∠3. between the two lines? 1 𝑦 = 𝑥 3 3𝑥 + 𝑦 = 2

Angle sum Triangle 180° Quadrilateral 360° 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 ∠𝐷𝐴𝐶 & ∠ DCA between ∠6 system. What [40°, 70°, 90°] and ∠5? If is the ∠5= 21 ⁰, relationship solve for ∠2. between the two lines? 1 𝑦 = 𝑥 3 3𝑥 + 𝑦 = 2

Angle sum Triangle 180° Quadrilateral 360° 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 ∠𝐴𝐵𝐶 & ∠ ADC between system. What ∠1and ∠7? If is the ∠1= 3 ⁰, solve relationship for ∠7. between the two lines? 1 𝑦 = 𝑥 4 4𝑥 + 𝑦 = 2

Angle sum Triangle 180° Quadrilateral 360° Pentagon (think ) y= mx + b defines linear

Math Review November 11, 2014 1. Given the angles below, solve for ∠𝑋 2. What is the relationship 3. Graph the following between ∠4 system. What and ∠8? If is the ∠4= 63 ⁰, relationship solve for ∠7. between the two lines? 1 𝑦 = 𝑥 3 3𝑥 + 𝑦 = 2

Angle sum Triangle 180° Quadrilateral 360° 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

 

y y

2  1  2   1  2

y= mx + b defines linear

Math Review September 15, 2014 1a. Determine area of square with side lengths of 2” 2. Find the midpoint between (-6, 24) and (2, 0) 3. Graph y= 1

x

1b. Determine perimeter of square with side lengths of 2” 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



r



+ 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