Geometry Angle Review Evening

Types of Angles

Introduction to Angles

Make sure your notes to answer the questions.

Multiple Choice

What kind of angle is this?

• Right Angle

• Acute Angle

• Obtuse Angle

• Straight Angle

Multiple Choice

What kind of angle is this?

• Right Angle

• Acute Angle

• Obtuse Angle

• Straight Angle

Multiple Choice

What kind of angle is this?

• Right Angle

• Acute Angle

• Obtuse Angle

• Straight Angle

Multiple Choice

What kind of angle is this?

• Right Angle

• Acute Angle

• Obtuse Angle

• Straight Angle

Multiple Choice

location with no size or shape

• point

• line

• ray

• plane

Multiple Choice

straight path extending infinitely in opposite directions

• point

• line

• ray

• plane

Multiple Choice

part of a line that starts at a point and extends infinitely in one direction

• line segment

• ray

• vertex

• parallel line

Multiple Choice

part of a line with two endpoints

• vertex

• line segment

• point

• ray

Opposite and congruent angles formed by the intersection of two lines.

​​Vertical Angles

Angles that have the same vertex, share a common side and do not overlap.

​​Adjacent Angles

Two angles are complementary if the sum of their measure is 90°

Complementary Angles

Two angles are supplementary if the sum of their measure is 180°

Supplementary Angles

Multiple Choice

Angles that have the same vertex, share a common side, and do not overlap.

• congruent angles

• complementary angles

• adjacent angles

• vertical angles

Multiple Choice

Angles whose sum of their measures that equals 90°

• congruent angles

• complementary angles

• adjacent angles

• supplementary angles

Multiple Choice

Angles whose sum of their measures equals 180°

• congruent angles

• complementary angles

• adjacent angles

• supplementary angles

Multiple Choice

Opposite angles formed by the intersection of two lines. These angles are always congruent

• vertical angles

• complementary angles

• adjacent angles

• supplementary angles

Segment Addition

The parts have to add up to equal the whole. This also means we could use the whole and subtract one of the parts to find the other part.

Open Ended

What is the missing measurement?

Multiple Choice

Find DE

• 5
• 6
• 20
• 21

Multiple Choice

Use the figure to write and solve an equation for x.

• 5
• 6
• 7
• 8

Multiple Choice

Use the figure to write and solve an equation for x.

• 5
• 6
• 7
• 8

Angle Addition Postulate
Part + Part= Whole

Segment Addition: Solving for x.

We can also use Segment Addition to set up equations that we can then solve. The equation would say _____ + _____ = whole, and the two parts would go in the blanks.

Using Angle Addition to Solve for x.

Start by identifying which pieces of information go where in the picture. Then set up an equation that shows _____ + _____ = whole, where the two parts go in the blank and are set equal to the whole.

Multiple Choice

Calculate m∠ABC.

• 45°

• 60°

• 105°

• 15°

Multiple Choice

Find m∠A.

• 25°

• 30°

• 35°

• 90°

Multiple Choice

Given m∠QST = 135°, find the value of x.

• 15
• x = 28

• x = 27

• x = 29

Angle Types We Know

• We have been discussing 4 types of angles. They are:

• Alternate Interior

• Alternate Exterior

• Same Side Interior

• Same Side Exterior

Corresponding Angles

Corresponding angles are angle that are in the same location but in different intersections.

Alternate Interior Angles

Alternate Exterior Angles

Consecutive Interior Angles

Multiple Choice

If angle P measures 60 degrees, what is the measure of angle C?

• 60 degrees

• 30 degrees

• 120 degrees

Multiple Choice

Find the measure of angle A.

• ∠A=82°

• ∠A=98°

• ∠A=180°

• ∠A=8°

Multiple Choice

Find the measure of angle L.

• ∠L=51°

• ∠L=129°

• ∠L=180°

• ∠L=39°

Multiple Choice

Find the measure of angle M.

• ∠M=47°

• ∠M=133°

• ∠M=180°

• ∠M=33°

Multiple Choice

Angle 1 = 27^o

Find the measure of angle 4

• 27^o

• 153^o

• 63^o

• 90^o

Multiple Select

Select the images that represent alternate interior angles.

Multiple Select

Select the images that show alternate exterior angles.

Multiple Select

Zoom in on the picture. What angle are consecutive interior angles?

• $$\angle1\ and\ \angle4$$

• $$\angle3\ and\ \angle5$$

• $$\angle7\ and\ \angle8$$

• $$\angle4\ and\ \angle6$$

Multiple Select

Which images represent corresponding angles?

Multiple Choice

A transformation that “turns” a figure around a fixed point at a given angle and a given direction.

• rotation

• translation

• reflection

• dilation

Multiple Choice

Translations, reflections and rotations are all known as ________________________.

• Geometry

• Transformations

• Congruent

• Ratios

Multiple Choice

A slide is also called a _________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

A flip is also called a _________.

• Translation

• Reflection

• Rotation

• Transformation

Multiple Choice

Congruent means...

• The same angles.

• The same size and same shape.

• Equal to.

• The same transformation.

Multiple Choice

Describe the Transformation

• Translation

• Reflection

• Rotation

Multiple Choice

Describe the transformation in the image.

• Translation

• Reflection

• Rotation

Multiple Choice

What is this picture an example of?

• Reflection

• Translation

• Rotation

• Dilation

Multiple Choice

Name the transformation.

• Translation

• Reflection

• Rotation

Multiple Choice

Identify the transformation from ABC to A'B'C'.

• 90^o clockwise rotation
• 90^o counter clockwise rotation
• Reflection across the y-axis
• Reflection across the x-axis

Classify by Sides

• All three sides alike = equilateral

• Two sides alike = isosceles

• No sides alike = scalene

Classify by Angles

• Two angles in a triangle are always acute so it's the third angle that helps us classify the triangle

• Acute - all 3 angles are less than 90 degrees

• Obtuse - one angle is greater than 90 degrees (and the other two are acute)

• Right - one angle is 90 degrees (and the other two are acute)

Multiple Choice

Please classify the triangle by its angles

• acute

• obtuse

• right

Multiple Choice

Please classify the triangle by its sides

• equilateral

• isosceles

• scalene

Multiple Choice

Classify the triangle by its sides and angles

• isosceles, right

• scalene, obtuse

• isosceles, acute

• scalene, right

• equilateral, obtuse

Multiple Choice

Classify the triangle by its sides and angles

• isosceles, acute

• scalene, obtuse

• scalene, right

• equilateral, obtuse

1800

m 2 + m 3

Triangle Angle Sum

Since every triangle has a sum of 180^o, to determine the value of the unknown angle in a triangle:

1. add the two known angles

2. subtract that sum from 180^o.

Fill in the Blank

What is the sum of the known angles?

Fill in the Blank

What is the value of the unknown angle?

Multiple Choice

find measurement of a missing angle (solve for x)

• x=140

• x=40

• x=180

Multiple Choice

Solve for x. (Hint: 70 + 60 + 8x + 2 = 180; combine like terms and solve for x)

• 16

• 11

• 50

• 6

Angle Sum of a Triangle

• The sum of the measures of the interior angles of a triangle is 180^o.

• <1 + <2 + <3 = 180

Remember:
You can make multiple triangles of different sizes with one set of angles.
However, if you are given a set of side lengths, you are given the dimensions of a single triangle.

Multiple Choice

Does a triangle with these side lengths exist?
33, 16, 17

• Yes
• No
• I don't know.

Multiple Choice

Which set of side lengths will NOT make a triangle?

• 3, 4, 5
• 1, 3, 4
•  3, 5, 7
• 2, 8, 9

Multiple Choice

Does a triangle with these side lengths exist?

15, 12, 9

• Yes

• No

Multiple Choice

Can the sides of a triangle have lengths 4, 11, and 13?

• Yes

• No

Multiple Choice

Can the following side measures form a triangle?

3, 5, 8

• Yes

• No