Geometry

47 Line notation and relationships46 Measure , draw, and name angles45 Angle Pairs44 Identify polygons and quadrilaterals43 Solids42 Translation, rotation, reflection, and dilations41 Missing angles in triangles40 Classify s and s39 Similarity and Congruence38 Similar triangles and proportions37 WP: Similar triangles and proportionsIce Cream Answer

Puzzle - PresidentThe 22nd and 24th president of the United States had the same mother and the same father, but they were not brothers. How is this possible?

Who was this???

47a Line notation and relationships

Use the figure to name a line containing point K.

Answer: The line can be named as line a.

There are three points on the line. Any two of the points can be used to name the line.

A line can be named by a lower case letter or by two points on that line.

47b Line notation and relationships

Ray

Line

Means Perpendicular (90°)

Means “Line” (Has No Endpoints)

Means “Ray” (Has one endpoint)

— Means “Line Segment” (Has two endpoints – Has a length)

Means “Perpendicular” (Meets in a 90° angle or Right )

|| Means “Parallel” (Follow same direction – Never intersect)

Skew lines are in different planes and never intersect

***If you have a protractor, bring it to class!***

If a daddy bull weighs 1,200 pounds and eats 12 bales of hay each day, and a baby bull, who weighs 300 pounds, eats 3 bales of hay each day, then how much hay should a mommy bull eat if she weighs 800 pounds?

Puzzle - Know bull

46a Measure, draw, and name angles

An angle is usually named by 3 noncollinear points

Angles can be named with three points on the angle with the vertex in the middle or by the vertex point if it is the only angle with that vertex.

L

M N

LMN or NML or M are all correct

MLN or L etc are NOT correct

When referring to an angle you may also mark it with an arc.

1

An angle may also be named by a number such as above. 1

46b Measure, draw, and name angles

Acute – Less than 90°

Right – Exactly 90° – Marked by a Small

Obtuse – Greater than 90° but less than 180°

Straight – Exactly 180°

Complementary s – Two angles that add up to 90° (Right)

Supplementary s – Two angles that add up to 180° (Straight)

Adjacent s – Two angles with a common sideand a common vertex

A complete circle = 360°

46c Measure, draw, and name angles

Measure each angle named and classify it as right, acute, or obtuse.

a. CZD

b. CZE

c. DZX

Answer: 150, obtuse

Answer: 90, right

Answer: 30, acute

46d Measure, draw, and name anglesWhat is the measure of the following angle?

Puzzle

What orchestral device is not blown, bowed, plucked, or struck?

45a – Angle pairs

Linear pair – Two angles that form a straight angle (180)Vertical Angles – Angles directly across from each other

when two lines intersect – Vertical angles are congruent ()

Vertical angles

DE

F G

DEF and FEG form a Linear Pair

*Complementary s – Two angles that add up to 90°

*Supplementary s – Two angles that add up to 180°

*Adjacent s – Two angles with a common side And a common vertex

Puzzle - Impossible Triangle

44a Identify polygons and quadrilaterals

3 sides - Triangle

4 sides - Quadrilateral

5 sides - Pentagon6 sides - Hexagon

7 sides - Heptagon or septagon*

8 sides - Octagon

9 sides - Nonagon

10 sides - Decagon

11 sides - 11-gon

12 sides - Dodecagon*

13 sides - 13-gon

Polygon – “Poly” means many, “gon” means angles

Is a circle a polygon? No

*These are the most likely polygons to be named on your final exam….

Know these!!!!!

44b Identify polygons and quadrilaterals

Parallelogram – Both pairs of opposite sides ||

Properties

Opposite sides are Opposite s are

>>

>>> >

44c Identify polygons and quadrilaterals

Rectangle – Quadrilateral with 4 Rt. s

Properties

Opposite sides are - 2 pairs of || sides

44d Identify polygons and quadrilaterals

Rhombus – Quadrilateral with all four sides

Properties

All properties of a parallelogram

Diagonals are

44e Identify polygons and quadrilaterals

Square – Both a rhombus and a rectangle

Properties

Four sides and four s

44f Identify polygons and quadrilaterals

Trapezoid – Exactly ONE pair of || sidesThe || sides are called the basesThe non-|| sides are called legs

Isosceles Trapezoid – One pair of || SidesBoth legs are congruent

||||

Both pairs of base angles are

44g Identify polygons and quadrilaterals

A kite is basically two isosceles triangles

Properties

Diagonals form Rt. Angles

Puzzle

What is it you sit in, sleep in, and brush your teeth with?

43a SolidsPolyhedron = “Poly” means many, “hedron” means faces

Faces = Flat surfaces (polygons)

Edges = Line where two faces meet

Vertices = Point or corner where edges meet

Prism = Has two bases that are ||Named by the shape of the base

Pyramid = Has only one base and comes to a pointNamed by the shape of the base

Is this a polyhedron?

NO

FacesEdgesVertices

612

8

A net is simply a shape unfolded

=

=

43b Solids

43c Solids

43d Solids - ActivityTetrahedron

Faces Vertices Edges

Cube

Faces Vertices Edges

Octahedron

Faces Vertices Edges

Icosahedron

Faces Vertices Edges

Dodecahedron

Faces Vertices Edges

These shapes are called the Platonic Solids.

Why are they special?What to they mean?

Clock Trick

42a Trans, Rot, Refl, & Dilation

Remember that ordered pairs describe a location in terms of Remember that ordered pairs describe a location in terms of x and y such that (x,y).x and y such that (x,y).

These are always in alphabetical order

Where is point A and M located? A (-3,4) M(1,2)

Also recall the quadrant values

II I

III IV

42b Trans, Rot, Refl, & DilationTranslation is simply a movement of a shape

Ex. Points (–8, 4), (–8, 9), (–2, 9), and (–2, 4) form a quadrilateral. Which graph displays the quadrilateral and its dotted translation 5 units to the right and 6 units down?

42c Trans, Rot, Refl, & Dilation

Rotation is simply turning an object

Ex. Draw the rotation image of the figure for a rotation of 270clockwise around turning point D.

42d Trans, Rot, Refl, & DilationReflection simply “flips” or “reflects” an image over a line

42e Trans, Rot, Refl, & Dilation

Dilation is when something changes in sizeThink of your eyes dilating - The pupil changes size

The Scale Factor is by how much it changes size

Ex. The dotted triangle is the image of the solid triangle under a dilation with center (0,0). What is the scale factor?

42f Trans, Rot, Refl, & Dilation

Quiz tomorrow on sections 83-7983 Line notation and relationships82 Measure , draw, and name angles81 Angle Pairs80 Identify polygons and quadrilaterals79 Solids78 Translation, rotation, reflection, and dilations

15 Questions - 15 Points

Puzzle

If I have one and a half dozen kids, how many children do I have.

(By the way, this is not true)

41a Missing angles in a triangle

The sum of the interior angles of a triangle = 180°

A

B

C

A + B +C = 180°

If mA=32 and mB= 105, What is the measure of C?

32 + 105 + C = 180°

The measure of C = 43°

32

105

C = 180 - 32 - 105C = 43

41b Missing angles in a triangle

Exterior

A

B

C

D

E•

•132°

x

Solve for x.

?48°

180-90-48= 42

x=42°

40 Classify s and s

My friends party……

A friend of mine has three kids

Product of their ages is 72

Sum of ages is house number

Oldest child loves strawberry ice cream

How old are his children?What is his house number?

40 Classify s and s

40a Classify s and s

Triangles be classified by the measures of their angles

Acute All angles are less than 90°

Right One angle measures 90 °

Obtuse One angle is greater than 90 °

40b Classify s and sTriangles can be classified by lengths of sides

Equilateral All sides and all angles are

Isosceles Two sides and two angles

Scalene No sides and no angles

Right Lengths a2+b2=c2

(c is the longest side)c

PuzzleCarry’s mother had a rather unusual fixation for naming her four children. The first child was named Quarter, the second child was named Dimeone and the third child was named Nicholas.

What was the fourth Childs name?

39a Similarity and congruence

Similar polygons ( ~ ) have corresponding angles and the corresponding sides are proportional. Same shape, different size.

AB

CD

W

X

YZ

Similarity Statement

ABCD~WXYZ

~

We can conclude:

A WB X

D ZC Y

WX

AB

XY

BC

YZ

CD

ZW

DA

Congruent polygons ( ) are exactly the same shape and size

39b Similarity and congruenceOne triangle is shown on the grid. Two coordinates for a second triangle are also shown on the grid. Using the two points on the graph, which coordinates will create another triangle that is similar to the triangle that is shown?

[A] (–6, –2)

[B] (–6, 5)

[C] (–6, –7)

[D] (–6, –5)

39c Similarity and congruenceWhich two figures are similar but not congruent?

[A] 1 and 5 [B] 3 and 5 [C] 2 and 4 [D] 2 and 3

Triangles BFC and QVU are similar. Write a proportion correctly identifying the corresponding sides?

39d Similarity and congruenceWhich statement is false?

[A] g k [B] a f [C] a f [D] a k

39e Similarity and congruenceCDE ~ HGF . Find the measure of x.

x=60°

Puzzle

Has anyone figured out the strawberry ice-cream question yet?

A friend of mine has three kids

Product of their ages is 72

Sum of ages is house number

Oldest child loves strawberry ice cream

How old are his children?What is his house number?

38a Similar s and proportions

~ Polygons have same shape, and proportional sides.

A

B

CD

W

YZ

~2 3

69

34.5

AD=2 and WZ=3,

If AB=6, what is the length of WX? ___

X

9

If YZ=4.5, what is the length of CD? ____3

38b Similar s and proportionsGiven that ABC ~ DEF, solve for x and y.

If ABC ~ DEF, BC = 3 feet, EF = 12 feet, and FD = 1 foot, find AC.

A

B

CD

E

F

12

1

3

?

38c Similar s and proportions

ABC and XYZ are similar. If AB, BC, and AC are 6 inches, 11 inches, and 15 inches respectively, and XY is 9 inches, find XZ to the nearest tenth.

A

B C Y

X

Z

6

11

15 9

?

Puzzle

Don’t read the words below, just say the color they are printed in.

REDYELLOWGREENBLUERED

BLUEYELLOWGREEN

37a WP: Similar s and proportions

Standing next to each other, a woman casts a 51.2-inch shadow and her 46-inch-tall daughter casts a 36.8-inch shadow. What is the height of the woman to the nearest inch?

51.2

46

36.8

x

37b WP: Similar s and proportionsTwo ladders are leaning against a wall at the same angle as shown. How long is the shorter ladder?

37c WP: Similar s and proportions

Ruby wants to find the height of the tallest building in her city. She stands 399 feet away from the building. There is a tree 32 feet in front of her, which she knows is 15 feet tall. How tall is the building? (Round to the nearest foot.)

37d WP: Similar s and proportions

37e WP: Similar s and proportionsMichele wants to measure the height of the streetlight outside her house. She places a mirror on the ground 46 feet from the streetlight, then walks backward until she is able to see the top of the streetlight in the mirror. Her eyes are 5.4 feet above the ground, and she is 12 feet from the mirror. What is the height of the streetlight to the nearest tenth of a foot?

4612

5.4x

37a WP: Similar s and proportions