Definition and Drawing for:

Point

Definition and Drawing for:

line

Definition and drawing for:

plane

Definition and drawing for:

line segment

Definition and drawing for:

ray

Notation for:

segment BC

Notation for:

ray BC

Notation for:

line BC

Notation for:

angle ABC

Notation for:

triangle ABC

Definition of union

(A union B)

Definition of intersection

(A intersect B)

[image]

What term describes line m and n?

[image]

what term describes lines n and m?

[image]

Interior angles

[image]

Exterior angles

[image]

Alternate Interior angles

If lines are parallel, supplementary or congruent?

angles 3 and 6

angles 4 and 5

congruent

[image]

Alternate exterior angles

If lines are parallel, supplementary or congruent?

angles 1 and 8

angles 2 and 7

congruent

[image]

Corresponding angles

if lines are parallel, supplementary or congruent?

angles 1 and 5

angles 2 and 6

angles 3 and 7

angles 4 and 8

Congruent

[image]

Consecutive interior

If lines are parallel, supplementary or congruent?

angles 3 and 5

angles 4 and 6

What is the converse of:

If the light is red, then you cannot drive.

If you cannot drive, then the light is red.

What is the inverse of:

If the light is red, then you cannot drive.

What is the contrapositive of:

If the light is red, then you cannot drive.

If you can drive, then the light is not red.

[image]

What term describes point M?

average the two x-values of the endpoints to get the x-coordinate of the midpoint

average the two y-values of the endpoints to the y-coordinate of the midpoint

add x's and divide by 2

add y's and divide by 2

What does the 

Triangle Sum Theorem

state?

180 degrees

(triangle sum theorem)

What is the Pythagorean Theorem?

What kind of triangle can you apply it to?

[image]

What is a possible congruence statement for this diagram?

[image]

What rule could you use to prove these triangles are congruent?

[image]

What rule could you use to prove these triangles are congruent?

AAS

[image]

What rule could you use to prove these triangles are congruent?

[image]

What rule could you use to prove these triangles are congruent?

Congruent triangles have 

(congruent/ proportionate/ different) sides and 

(congruent / proportionate/ different) angles.

Similar triangles have 

(congruent/ proportionate/ different) sides and 

(congruent / proportionate/ different) angles.

In the image below, what property explains why side AM is congruent to side AM?

[image]

What reason explains why angle APB is congruent to angle KPE?

[image]

What reason explains why angle ABD is congruent to angle DBC?

[image]

If side QX is parallel to RT, what reason explains why angle Q is congruen to angle T?

[image]

If side DC is parallel to AB, what reason explains why angle 2 is congruent to angle 4?

[image]

What justifications and reasons explain why ΔABC is similar to ΔADE?

[image]

jusfitications: corresponding angles

rule: AA

What rule explains why the triangles below are similar?

[image]

SAS

sides are proportionate and angles are congruent

5/10 = 10/20

What rule explains why the triangles below are similar?

[image]

Rule: SSS

sides are proportionate

2/4 = 3/6= 4/8

1) It is parallel to the side of the triangle it is across from.

2) It is half the length of the triangle it is across from.

Properties of a parallelogram

(sides, angle, diagonals)

-opposite sides are congruent

-opposite angles are congruent

-consecutive angles are supplementary

-diagonals bisect each other (share a common midpoint)

Properties of a rectangle

(sides, angles, diagonals)

-congruent angles (all 90°) OR consecutive sides are perpendicular

-congruent diagonals

-composed of 4 isosceles triangles

**plus all properties of a parallelogram

Properties of a rhombus

(sides, angle, diagonals)

-all sides are congruent

-diagonals are perpendicular

-diagonals bisect vertex angles

-composed of 4 right triangles

**plus all properties of a parallelogram

Properties of a square

(sides, angles, diagonals)

Combines properties of rectangle and rhombus.

Properties of rectangle: congruent angles and diagonals

Properties of a rhombus: congruent sides, perpendicular diagonals, diagonals bisect vertex angles

Composed of 4 45-45-90 triangles

Properties of a trapezoid

(sides and angles)

NOT A PARALLELOGRAM!!

-one pair of parallel sides called bases

-angles between bases are supplementary

NOT A PARALLELOGRAM!!

-one pair of parallel sides called bases

-one pair of congruent sides called legs

-angles between bases are supplementary

-base angles are congruent

-congruent diagonals

For a regular pentagon, calculate the measure of:

a) measure of 1 exterior angle

b) measure of 1 interior angle

c) sum of interior angles

a) measure of 1 exterior angle:  360/5 = 72°

b) measure of 1 interior angle: 180-72 = 108°

c) sum of interior angles: 108·5  or 180(5-2) = 540°

For circle O, what type of angle is this?

[image]

What type of angle is this?

[image]

What kind of angle is angle B?

[image]

What is the relationship between an inscribed angle and the arc it cuts out (as in the diagram below)?

[image]

The arc is twice the measure of the inscribed angle

The measure of arc AC is twice the measure of angle B

What is the relationship between a central angle and the arc it cuts out (as in the diagram below)?

[image]

The arc measure equals the angle measure.

The measure of arc AC is the equal to the measure of angle O

What is the measure of the angle, x, in the diagram below?

[image]

add the arcs and divide by 2!

70 + 170 = 240 / 2 = 120°

What is the measure of angle A in the diagram below?

[image]

subtract your arcs and divide by 2!

120 - 40 = 80/2 = 40° 

What is the length of the segment labeled with x in the diagram below?

[image]

multiple lengths on same chord

3·x= 6·4

x = 8

What is the value of x in the diagram below?

[image]

outside · whole = outside · whole

x · x = 5 · (5+7)

x² = 5(12)

x²  = 60

x = √60 ≈  7.7

What is the length of x in the diagram below?

[image]

outside · whole = outside · whole

18 (x + 18) = 16 (16+24)

18x + 324 = 16 (40)

18x + 324 = 640

x ≈ 17.6

What type of segment is AB below?

[image]

What type of line is AB below?

[image]

What kind of line is LP below?

[image]

What is the slant height of the square pyramid below?

[image]

The slant height of a pyramid or cone can be found using the Pythagorean Theorem.

c - slant height

a- height of the solid

b- half the length of the side of the base (or radius for a cone)

c^{2 =} 30² + 16²

c^{2 =} 900 + 256

c² = 1156

c = √1156 = 34

What is the height of the cylinder below?

[image]

The height is ALWAYS the distance between the bases:

15 inches

What is the area of the right triangle below?

[image]

Area = ½·base·height

Area = ½·8·6

A= 24 

What is the circumference of the circle below, in terms of ∏?

What is the area of the circle below, in terms of ∏?

[image]

C = 2∏r

A= ∏r²

C = 2∏(9) = 18∏

A = ∏(9)² = 81∏

What is the area and perimeter of the square below?

[image]

A = s²

p = 4s (s+s+s+s)

A= 36

p = 24

What type of transformation is depicted below?

[image]

What type of transformation is this?

[image]

What type of transformation is this?

State the rule for it.

[image]

Translation

(x,y) → (x - 4,y + 5)

What type of transformation is this?

[image]

What type of transformation is this?

[image]

Does this image have point symmetry?  line symmetry?

[image]

No point symmetry- when you rotate it 180° it is not the same image.

Vertical line of symmetry

 [image]

Does this image have point symmetry?  line symmetry?

[image]

Yes, it has point symmetry.  When you rotate it 180°, it is the same image.

It has 4 lines of symmetry.

[image]

How many lines of symmetry does a regular pentagon have?

Does it have point symmetry?

5 - for a regular polygon the number of sides equals the number of lines of symmetry

[image]

No point symmetry- it does not have an even number of sides